Datasets:
Tasks:
Image-Text-to-Text
Modalities:
Image
Formats:
imagefolder
Languages:
English
Size:
< 1K
ArXiv:
License:
| {"sample_id":"path_test_cell000_seed00000000","image":"images/path_test_cell000_seed00000000.png","image_sha256":"ee8c8467481851f1744cda25090203fb8982a531f2cbea2b5653811435823497","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, B, G, L, M, N}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, G), (B, M), (L, N)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell000_seed00000001","image":"images/path_test_cell000_seed00000001.png","image_sha256":"26adfe157c845631b79e7c7d7c9836e5d26a190e3d849188a7773f4c83dba222","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {E, G, H, J, N, R}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(E, G), (H, R), (J, N)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell000_seed00000002","image":"images/path_test_cell000_seed00000002.png","image_sha256":"fb439328f0eb342d1bdf79c7f2adb49ce1ae6d33527aa3f1bf9ac92cd3c9e2c4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {H, J, K, M, N, P}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(H, P), (J, K), (M, N)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell000_seed00000003","image":"images/path_test_cell000_seed00000003.png","image_sha256":"9d4189fcbc49f2511721e60f0d8d722344f32ca3f30633b14a0d764a34efb504","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {F, G, J, K, L, X}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(F, L), (G, J), (K, X)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell000_seed00000004","image":"images/path_test_cell000_seed00000004.png","image_sha256":"92662c08d6cda4f60e699e1131e2b128abbb88d14ca95893ef1ae2d1aadf6969","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {F, L, M, R, S, U}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(F, R), (L, M), (S, U)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell001_seed00001000","image":"images/path_test_cell001_seed00001000.png","image_sha256":"a34250c11da825284c613dd652808ea01e14ca35e163943711aef05c1f6378d1","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {C, G, I, J, N, Q}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(C, I), (G, Q), (J, N)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell001_seed00001001","image":"images/path_test_cell001_seed00001001.png","image_sha256":"7b5efea9fd0e6b96a3b1c28aee43a959228c81867ac0c81f1789659f99fb16a4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, C, I, L, T, U}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, I), (C, U), (L, T)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell001_seed00001002","image":"images/path_test_cell001_seed00001002.png","image_sha256":"a1f3df2e35dc465e0b8118ff2a89fdef90245ab05f65622dace673d09b5768a5","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {E, I, N, P, U, V}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(E, U), (I, P), (N, V)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell001_seed00001003","image":"images/path_test_cell001_seed00001003.png","image_sha256":"04a641e25a5b00edac2536abc09554c242decc5ee8f29d06537fb7129f3a8ead","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {H, J, N, R, X, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(H, R), (J, N), (X, Z)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell001_seed00001004","image":"images/path_test_cell001_seed00001004.png","image_sha256":"272a81c956f58cbe6fa3836ddb48e44cff433f1478d19bd6dee884dec7155f77","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {D, G, I, J, O, R}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(D, R), (G, I), (J, O)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell002_seed00002000","image":"images/path_test_cell002_seed00002000.png","image_sha256":"61eaa4a31c6cd2f4fe3bc54474b147ec7d8428a823c6bfef65c9dfdd8ccccaee","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, I, K, P, V, X}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, V), (I, X), (K, P)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell002_seed00002001","image":"images/path_test_cell002_seed00002001.png","image_sha256":"4d61f51b1767944de66a88ee532214754c74aba96d50ecae6451b2bf2e258008","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {F, I, J, P, R, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(F, R), (I, J), (P, Z)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell002_seed00002002","image":"images/path_test_cell002_seed00002002.png","image_sha256":"13bc42e7e4a767cf91683b7ad36a3d4364b6d3043f1b17f9b40536a70e3194e8","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, D, H, P, Q, U}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, P), (D, H), (Q, U)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell002_seed00002003","image":"images/path_test_cell002_seed00002003.png","image_sha256":"6dbb1a96bed22978f646f796e95f543668434e86cbf89f91533bc517160c2927","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {L, M, N, Q, R, S}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(L, Q), (M, R), (N, S)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell002_seed00002004","image":"images/path_test_cell002_seed00002004.png","image_sha256":"19400df6bd4d418af0546a7a3aaa173080216bdf10de4c63327d9a2e39480b4a","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {D, F, S, T, W, X}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(D, T), (F, X), (S, W)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell003_seed00003000","image":"images/path_test_cell003_seed00003000.png","image_sha256":"2c2d2a6cb567d2be738d32683b9fe9d7cb9ef43d9a222ed901035f4cfa2c98f4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {C, G, H, K, N, P}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(C, K), (G, P), (H, N)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell003_seed00003001","image":"images/path_test_cell003_seed00003001.png","image_sha256":"238ecb402e57f053d8b79ea93bf0461c68e8a907c430cf88bfb9aeefb680ec13","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {C, J, K, L, S, T}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(C, S), (J, K), (L, T)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell003_seed00003002","image":"images/path_test_cell003_seed00003002.png","image_sha256":"7c3e38dbb08dc6b4c77bb13c7ade884acbab871e8becff6d89e2aa36443bfe36","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, C, H, K, M, O}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, M), (C, H), (K, O)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell003_seed00003003","image":"images/path_test_cell003_seed00003003.png","image_sha256":"310bb04cb12529f126ab5ba1c9b5a2047ebd34b1c00b99a28cefb45be8b56f6b","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, C, G, T, W, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, G), (C, W), (T, Z)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell003_seed00003004","image":"images/path_test_cell003_seed00003004.png","image_sha256":"06828c415f6f71b933d9ae1df30058d3b4d22f148883622c2e1ab48074997773","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, E, G, N, T, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, N), (E, T), (G, Z)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell004_seed00004000","image":"images/path_test_cell004_seed00004000.png","image_sha256":"62795b1e8488920dabc9d592344d01ea3575366ceb7cafba208e6f9b116f2bc8","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, G, J, M, O, V}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, J), (G, V), (M, O)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell004_seed00004001","image":"images/path_test_cell004_seed00004001.png","image_sha256":"28eb1bd86003512aefd350059fe87ccc2c968c3b867290fcfdffc59b76168d4c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {E, F, M, P, Y, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(E, P), (F, Z), (M, Y)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell004_seed00004002","image":"images/path_test_cell004_seed00004002.png","image_sha256":"e53acb3ddb0706f44aac448f21ff86e5259747f5e91df9ac7ccfc0932df7c94d","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {K, O, P, R, U, X}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(K, U), (O, P), (R, X)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell004_seed00004003","image":"images/path_test_cell004_seed00004003.png","image_sha256":"3419f4ad12a1c70a1edce22f3c43afb8ea252eb7d7e11737ef61123979ff6c41","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {C, D, J, M, Y, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(C, Y), (D, M), (J, Z)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell004_seed00004004","image":"images/path_test_cell004_seed00004004.png","image_sha256":"4f5e06d2259c2f075eb1933d7c2f36106d7b3867ea3c49520b781c276b7195aa","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, C, G, R, S, W}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, R), (C, S), (G, W)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell005_seed00005000","image":"images/path_test_cell005_seed00005000.png","image_sha256":"4dae039cb70b7f07e13b0af435bdc356715fbf212f150372b267935782439dc3","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, K, M, N, Q, V}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, K), (M, N), (Q, V)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell005_seed00005001","image":"images/path_test_cell005_seed00005001.png","image_sha256":"2548ccaee836a700e7fc80e69a6cb8cfb835fe0cad2ac08bc37b14e13935bf78","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, B, E, K, T, Y}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, T), (B, K), (E, Y)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell005_seed00005002","image":"images/path_test_cell005_seed00005002.png","image_sha256":"6391da033b439faed482ba6ccad862040618b33c17411c6efdc034ddd7b3d402","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {C, E, G, J, P, T}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(C, T), (E, G), (J, P)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell005_seed00005003","image":"images/path_test_cell005_seed00005003.png","image_sha256":"d6867a0955bd7d240ff88407001f391e407de8057c46160aa656fc60fc1b8dff","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, H, L, Q, S, T}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, L), (H, T), (Q, S)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell005_seed00005004","image":"images/path_test_cell005_seed00005004.png","image_sha256":"14a1d8e5a73175705bab012ef443c71a62bff7b537d6e00bc647eebbc9fbe33f","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, D, H, R, U, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, R), (D, Z), (H, U)}.","difficulty":"easy","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell006_seed00006000","image":"images/path_test_cell006_seed00006000.png","image_sha256":"99ac056c33e95e240b8dddec60a7d573b133ddd6e5d3422c10de08c1321bb5d8","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {20, 24, 40, 57, 64, 66}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(20, 57), (24, 66), (40, 64)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell006_seed00006001","image":"images/path_test_cell006_seed00006001.png","image_sha256":"a4499b479c00deeeccfec8b2482fb05d473aaaa94f3e1e0b46416f4f5ff91028","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {7, 21, 26, 31, 47, 71}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(7, 26), (21, 47), (31, 71)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell006_seed00006002","image":"images/path_test_cell006_seed00006002.png","image_sha256":"98c1cc308290156fb4aee275a17dd5f3018fc35e9eed7b4ba04af48c7c37724b","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {4, 44, 69, 78, 80, 98}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(4, 69), (44, 80), (78, 98)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell006_seed00006003","image":"images/path_test_cell006_seed00006003.png","image_sha256":"a79fec0e973b47638a374bd167d70bf3f4475fee382dc28c92222a6ce766a8ed","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {11, 23, 65, 66, 95, 99}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(11, 99), (23, 65), (66, 95)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell006_seed00006004","image":"images/path_test_cell006_seed00006004.png","image_sha256":"a9ed866d080ec63c366893256ed997ce692a1f5c07128aa8c2ef3848b6f5925d","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {22, 51, 52, 60, 67, 76}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(22, 52), (51, 67), (60, 76)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell007_seed00007000","image":"images/path_test_cell007_seed00007000.png","image_sha256":"3d7ab5d59a8c4aab8f22ef260c373cbaf463e4cdb5f669ad40ad90a63423dbf2","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {16, 45, 46, 49, 77, 96}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(16, 96), (45, 46), (49, 77)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell007_seed00007001","image":"images/path_test_cell007_seed00007001.png","image_sha256":"b8729798daccd5e892f3c1d38f92e94dbebed6639fad7ad0108593d74e55c7c4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {49, 57, 62, 63, 65, 86}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(49, 62), (57, 86), (63, 65)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell007_seed00007002","image":"images/path_test_cell007_seed00007002.png","image_sha256":"1b3388e38641cbfa32665ae69a357792e164e49e7cffdbff0c04829bb9971f5b","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {5, 15, 45, 50, 52, 92}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(5, 52), (15, 50), (45, 92)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell007_seed00007003","image":"images/path_test_cell007_seed00007003.png","image_sha256":"ac7539dc6d512b1e03451603d9b31351c9413262d38e5f45d03101d3c6ff8ed7","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {18, 36, 41, 53, 85, 98}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(18, 41), (36, 85), (53, 98)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell007_seed00007004","image":"images/path_test_cell007_seed00007004.png","image_sha256":"9f5684e4a0bb774b0ffd4d19f99ed7e87819f082e1a5e2e4a05c76031e989f3b","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {4, 14, 29, 71, 73, 92}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(4, 73), (14, 71), (29, 92)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell008_seed00008000","image":"images/path_test_cell008_seed00008000.png","image_sha256":"74b45dfc38535cd88cd8fece3520b2e4aa712aba9fe81a7c6218fa99afb6e65d","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {6, 12, 20, 53, 55, 86}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(6, 53), (12, 20), (55, 86)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell008_seed00008001","image":"images/path_test_cell008_seed00008001.png","image_sha256":"eae724e8f3f92378c5d64d7e9d60efe64982727b2758b77a27e1079ae047a5cb","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {24, 42, 47, 61, 90, 95}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(24, 42), (47, 61), (90, 95)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell008_seed00008002","image":"images/path_test_cell008_seed00008002.png","image_sha256":"aafe08899127d08ab3094d6096dbc6382702471b73593c2530cc4c6f2c21dfd6","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {2, 10, 20, 43, 51, 74}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(2, 74), (10, 51), (20, 43)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell008_seed00008003","image":"images/path_test_cell008_seed00008003.png","image_sha256":"b64d97bf70cb0503d9623a531ab8a0f16bfcfe11b912f6f3cb8fa33269752750","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {18, 20, 41, 73, 74, 79}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(18, 73), (20, 79), (41, 74)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell008_seed00008004","image":"images/path_test_cell008_seed00008004.png","image_sha256":"7ad254ddaa8a99a3e44f939574f002866f38eb17688503f822f594ee801e71d7","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {10, 31, 32, 35, 40, 96}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(10, 96), (31, 40), (32, 35)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell009_seed00009000","image":"images/path_test_cell009_seed00009000.png","image_sha256":"8143cf63a077feadca8dc1c449899366064ca22d01dc9ba8ab71213841c4b40c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {1, 9, 18, 20, 83, 98}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(1, 9), (18, 20), (83, 98)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell009_seed00009001","image":"images/path_test_cell009_seed00009001.png","image_sha256":"bcfcfa71b16ed2bfd0de5c63e6e7b7129a10666e9dfcda979a43edbfe6cc7d29","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {15, 31, 50, 53, 64, 81}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(15, 53), (31, 50), (64, 81)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell009_seed00009002","image":"images/path_test_cell009_seed00009002.png","image_sha256":"dffc8db8cd1b68ce16c2dc1d341205de4a60b1535efb0d0e0178323182acefed","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {40, 70, 74, 78, 90, 95}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(40, 95), (70, 78), (74, 90)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell009_seed00009003","image":"images/path_test_cell009_seed00009003.png","image_sha256":"dc81d196e06fd517a161af0b39a278bb48171b9f88a4afd0efec88a85e328c25","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {7, 22, 37, 48, 79, 94}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(7, 48), (22, 79), (37, 94)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell009_seed00009004","image":"images/path_test_cell009_seed00009004.png","image_sha256":"a18a36995e43e80a2fd9902f1a3d955984351df3c92e5a35efd8a3e23ffc28a4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {26, 50, 63, 65, 89, 91}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(26, 89), (50, 63), (65, 91)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell010_seed00010000","image":"images/path_test_cell010_seed00010000.png","image_sha256":"05e528286e1bd6086da4ef1140e65a5e1b62b66f6c037d76bdf51af0ca75e17b","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {22, 47, 64, 87, 95, 98}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(22, 98), (47, 64), (87, 95)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell010_seed00010001","image":"images/path_test_cell010_seed00010001.png","image_sha256":"3e43b47f6e5e2ba718e15c53d1bee25e81110d3ec48aa467c74108a31cff7491","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {25, 32, 48, 54, 88, 90}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(25, 88), (32, 54), (48, 90)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell010_seed00010002","image":"images/path_test_cell010_seed00010002.png","image_sha256":"2107c744edb5b04f8f710b508920121b8e1022aedcd0a65af03bc88bc8c4c1e4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {17, 22, 25, 59, 62, 68}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(17, 62), (22, 68), (25, 59)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell010_seed00010003","image":"images/path_test_cell010_seed00010003.png","image_sha256":"d08b765371f8928eaa9b151041e28fbf1c0b43629b0670e7c93aaaf43f59887c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {8, 14, 19, 48, 57, 88}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(8, 48), (14, 88), (19, 57)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell010_seed00010004","image":"images/path_test_cell010_seed00010004.png","image_sha256":"111ea26a024d296c1f11ecaa0623ae0470759580fad5cc65e6c626c468c27974","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {21, 32, 37, 46, 55, 73}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(21, 73), (32, 46), (37, 55)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell011_seed00011000","image":"images/path_test_cell011_seed00011000.png","image_sha256":"01254ffc768ee0ccb504eae3e7afb8ff5fe3f36cc1129e007647005af6ce4fe5","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {32, 37, 40, 60, 64, 87}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(32, 64), (37, 60), (40, 87)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell011_seed00011001","image":"images/path_test_cell011_seed00011001.png","image_sha256":"e5d90af360af92bbfae0b6724072329b0fa007afe376ee9ed67d2795124d71df","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {15, 29, 50, 52, 57, 93}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(15, 52), (29, 93), (50, 57)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell011_seed00011002","image":"images/path_test_cell011_seed00011002.png","image_sha256":"e26290e84f9797d0f5f64c66208541fa221b85fbd67ecdb2f272069fde0fda54","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {29, 55, 69, 70, 76, 94}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(29, 94), (55, 70), (69, 76)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell011_seed00011003","image":"images/path_test_cell011_seed00011003.png","image_sha256":"d1c2d8fa695e968f4cab753977b2ccc0a8ee192c70fdcb3369e51af3c52938aa","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {2, 3, 10, 15, 41, 88}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(2, 41), (3, 15), (10, 88)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell011_seed00011004","image":"images/path_test_cell011_seed00011004.png","image_sha256":"6bb3aada7c44af9742f69fec2747c18f308c897b4a27c62519b8187202025d39","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {1, 14, 44, 56, 87, 99}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(1, 14), (44, 56), (87, 99)}.","difficulty":"easy","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell012_seed00012000","image":"images/path_test_cell012_seed00012000.png","image_sha256":"dfe9132e2d026386c4b5eed703401a987af13bddcf41cd3d1d61b1160cc91416","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {butterfly, cat, diamond_shape, lightning, octopus, snowflake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(butterfly, snowflake), (cat, octopus), (diamond_shape, lightning)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell012_seed00012001","image":"images/path_test_cell012_seed00012001.png","image_sha256":"3c85982c8eee94307aaa5d7f8c93287c67d0ad2764e2764ffc5901ffd57f4271","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {apple, cloud, fire, fish, owl, star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(apple, fire), (cloud, fish), (owl, star)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell012_seed00012002","image":"images/path_test_cell012_seed00012002.png","image_sha256":"53aedf44dca120164410735f7ca2b3ffe532a754a78996b46c7212472beeffd0","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {cat, fire, lock, moon, mushroom, music_note}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(cat, fire), (lock, music_note), (moon, mushroom)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell012_seed00012003","image":"images/path_test_cell012_seed00012003.png","image_sha256":"96157c8bb194c7b0d63b06cd8a190bd84f42972942300f672d0db95668fe5f9f","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {carrot, cookie, crown, fish, lock, octopus}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(carrot, fish), (cookie, lock), (crown, octopus)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell012_seed00012004","image":"images/path_test_cell012_seed00012004.png","image_sha256":"9c094949c567bfd99bb12239f7eb6fa11db2a397d5ea4949f1685b2e1c960c3d","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {carrot, flower, hammer, key, rocket, snake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(carrot, key), (flower, hammer), (rocket, snake)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell013_seed00013000","image":"images/path_test_cell013_seed00013000.png","image_sha256":"e91911fee4aac32cff73ee3fd9fe80ace58e174fd113c8ae1ad9b6c25bde201e","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {banana, carrot, diamond_shape, fish, rocket, snake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(banana, diamond_shape), (carrot, snake), (fish, rocket)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell013_seed00013001","image":"images/path_test_cell013_seed00013001.png","image_sha256":"ed2052473f6f49b379d64265f5d3ab23fc7b18a67bcd13d9caf92e79144c0a00","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, cookie, key, lock, moon, owl}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, moon), (cookie, owl), (key, lock)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell013_seed00013002","image":"images/path_test_cell013_seed00013002.png","image_sha256":"a4133252498f1d7935f6fcfe8c562369f0c077abdd3e64975499d6192297709f","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {crown, frog, hammer, lock, music_note, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(crown, hammer), (frog, sun), (lock, music_note)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell013_seed00013003","image":"images/path_test_cell013_seed00013003.png","image_sha256":"28c30663e60e761fa989c2bd988eca37a0d25dd3d4687adee30a9b23b900c42c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, bee, cookie, fish, lock, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, lock), (bee, cookie), (fish, sun)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell013_seed00013004","image":"images/path_test_cell013_seed00013004.png","image_sha256":"a9236211d1f1fa2e717ff8001a531ae715b09c774af2940238f4ab755feb71d6","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {bee, carrot, cat, frog, gift, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(bee, carrot), (cat, sun), (frog, gift)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell014_seed00014000","image":"images/path_test_cell014_seed00014000.png","image_sha256":"81f27bb5358bb90a461d3c5058e74e698bff293df4eca5e8a736253aa6c7ea9a","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, fire, fish, gift, lock, mushroom}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, mushroom), (fire, fish), (gift, lock)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell014_seed00014001","image":"images/path_test_cell014_seed00014001.png","image_sha256":"e30739f010e75cbc62024b7e0a69bcf74d22059282a0eb21ea06f812b30557d6","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {apple, crown, flower, key, lock, pizza}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(apple, crown), (flower, lock), (key, pizza)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell014_seed00014002","image":"images/path_test_cell014_seed00014002.png","image_sha256":"a79bdab4468a69050027c9b95bee99b751e72b3adfed4f3f5a75378b36b9682c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {balloon, cat, cloud, dog, hammer, light_bulb}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(balloon, light_bulb), (cat, dog), (cloud, hammer)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell014_seed00014003","image":"images/path_test_cell014_seed00014003.png","image_sha256":"eeb450379362ea282784431ceda54cfbc5d8689415dc5424a8ca1321aa5934b2","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {balloon, cake, dog, fish, hammer, lightning}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(balloon, cake), (dog, hammer), (fish, lightning)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell014_seed00014004","image":"images/path_test_cell014_seed00014004.png","image_sha256":"27b59858fc1969ba4155b3569b0806b4da94e08080b5bee3e6683e0e2377efd3","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {crown, frog, gift, hammer, key, snowflake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(crown, gift), (frog, key), (hammer, snowflake)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell015_seed00015000","image":"images/path_test_cell015_seed00015000.png","image_sha256":"ed433ac3ea98f97a94ff9488efa400ef12df4a0cbd5cbcebffe3b525bf2cda6b","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {cookie, diamond_shape, fish, frog, lock, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(cookie, fish), (diamond_shape, frog), (lock, sun)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell015_seed00015001","image":"images/path_test_cell015_seed00015001.png","image_sha256":"29e7582bfa8caba9bef70088c0ffda4174cd30cab600a01cc9f3518b76f5ce7b","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {butterfly, cat, cloud, key, magnet, rocket}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(butterfly, cat), (cloud, key), (magnet, rocket)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell015_seed00015002","image":"images/path_test_cell015_seed00015002.png","image_sha256":"941e5d60e47d8ff218d0531dd66527eeb2ff32df9ab08dcfed015b7ab1c0de4f","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, dog, heart, key, octopus, snake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, heart), (dog, octopus), (key, snake)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell015_seed00015003","image":"images/path_test_cell015_seed00015003.png","image_sha256":"5541407de607d085da031d365e0b385c27bdfc7c9d879aef2e8f72964d8c813e","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {dog, frog, lock, mushroom, pizza, scissors}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(dog, lock), (frog, pizza), (mushroom, scissors)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell015_seed00015004","image":"images/path_test_cell015_seed00015004.png","image_sha256":"7ab4a4e9cffab405170e0e8e8ef41794f04bafe48c86c84de02181ceba049067","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {butterfly, cookie, crown, fire, flower, star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(butterfly, cookie), (crown, fire), (flower, star)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell016_seed00016000","image":"images/path_test_cell016_seed00016000.png","image_sha256":"22ba9a505801109c46f11e6cd924306d3fdfa6f33ae96ec8345f83fdd8a52beb","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, cloud, cookie, frog, heart, snowflake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, frog), (cloud, cookie), (heart, snowflake)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell016_seed00016001","image":"images/path_test_cell016_seed00016001.png","image_sha256":"2bdd4d48c14b062c1c1594f89ccb6c83f2a6041b1e8f9e0ff2132ba6a9abca85","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {apple, heart, lightning, moon, rocket, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(apple, moon), (heart, lightning), (rocket, sun)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell016_seed00016002","image":"images/path_test_cell016_seed00016002.png","image_sha256":"1b4f94dc91fe6117798a3aef7613fe156e5b8a17f2a09beae89be9d72497953a","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, butterfly, lock, octopus, owl, rocket}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, owl), (butterfly, rocket), (lock, octopus)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell016_seed00016003","image":"images/path_test_cell016_seed00016003.png","image_sha256":"15cd8d6ecde636253b36a794f77a835a7e2bba33417fed8479ffecdeea7e8711","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {butterfly, carrot, diamond_shape, fish, magnet, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(butterfly, sun), (carrot, diamond_shape), (fish, magnet)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell016_seed00016004","image":"images/path_test_cell016_seed00016004.png","image_sha256":"31176631f1ccaeef214b562c6205f9e2c82022ff7843988bce4e84de709231e1","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {cake, cookie, fire, frog, lock, pizza}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(cake, cookie), (fire, pizza), (frog, lock)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell017_seed00017000","image":"images/path_test_cell017_seed00017000.png","image_sha256":"43b09ca7c3bbdf9c0e3b857879d936aea4e451919ad55aaed3a4263fb4c24aa9","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {apple, blue_circle, cloud, dog, frog, scissors}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(apple, blue_circle), (cloud, frog), (dog, scissors)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell017_seed00017001","image":"images/path_test_cell017_seed00017001.png","image_sha256":"91e42682115bb410295dde71f5c8cdbf766f4f292b10c69f4041754bfcf1cb49","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {butterfly, cake, lock, owl, snake, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(butterfly, snake), (cake, sun), (lock, owl)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell017_seed00017002","image":"images/path_test_cell017_seed00017002.png","image_sha256":"e848d0f326e8ee0c8c1af30f9c9c3ad1f4bf730660aa016cf08d83d28cbb63a1","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {balloon, blue_circle, butterfly, flower, mushroom, scissors}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(balloon, blue_circle), (butterfly, flower), (mushroom, scissors)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell017_seed00017003","image":"images/path_test_cell017_seed00017003.png","image_sha256":"77505111be7adec4da73fff36a7185cd93a9d5d26710a0e953f86d8de66b4d9d","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {cat, light_bulb, lock, octopus, snake, snowflake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(cat, lock), (light_bulb, snake), (octopus, snowflake)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell017_seed00017004","image":"images/path_test_cell017_seed00017004.png","image_sha256":"631b6a70b8555cebaf5878b09d02296705e808b44001e266fcc972f5c389c4da","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {carrot, cat, cookie, diamond_shape, light_bulb, pizza}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(carrot, pizza), (cat, cookie), (diamond_shape, light_bulb)}.","difficulty":"easy","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell018_seed00018000","image":"images/path_test_cell018_seed00018000.png","image_sha256":"fe4d8334c3fc360e7d4c8f0278543d83a094b404d3658fd259b6dd33c1ceff0d","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_triangle, green_circle, green_square, red_circle, red_square, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_triangle, red_circle), (green_circle, yellow_triangle), (green_square, red_square)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell018_seed00018001","image":"images/path_test_cell018_seed00018001.png","image_sha256":"c5e89bb156440e7881ab0e840329794e764e1a14821f89752229b3b107fd6c1f","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_star, blue_triangle, green_square, green_triangle, orange_square, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_star, green_triangle), (blue_triangle, orange_square), (green_square, yellow_star)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell018_seed00018002","image":"images/path_test_cell018_seed00018002.png","image_sha256":"83ace4223c4a5c9f8ad18d08b3ad64c0b74111d7180d04bb1246efe15a751269","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_star, orange_square, red_diamond, yellow_circle, yellow_diamond, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_star, red_diamond), (orange_square, yellow_star), (yellow_circle, yellow_diamond)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell018_seed00018003","image":"images/path_test_cell018_seed00018003.png","image_sha256":"e9209b1c069b28affa15d8c97a94d3ce3fdfc12b0399a4ac3318ce0caee87dd5","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {purple_square, purple_triangle, red_hexagon, red_triangle, yellow_circle, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(purple_square, yellow_star), (purple_triangle, yellow_circle), (red_hexagon, red_triangle)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell018_seed00018004","image":"images/path_test_cell018_seed00018004.png","image_sha256":"2e80fc610ca71d922b34196621acbfce42a819eca6d434f806d43e989c308b68","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {green_square, orange_hexagon, purple_diamond, red_diamond, red_star, yellow_circle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(green_square, orange_hexagon), (purple_diamond, red_diamond), (red_star, yellow_circle)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell019_seed00019000","image":"images/path_test_cell019_seed00019000.png","image_sha256":"385d39d046414200a0ad7558a206041b5fdfa1645b3b9d117ae9ee9ff0fab1f8","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_hexagon, green_square, orange_triangle, red_circle, red_square, yellow_circle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_hexagon, green_square), (orange_triangle, red_square), (red_circle, yellow_circle)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell019_seed00019001","image":"images/path_test_cell019_seed00019001.png","image_sha256":"0e425a3b5146062509aaab1668170827ad70544db21e3230f1df13f82a94d7be","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_square, green_hexagon, green_star, green_triangle, purple_hexagon, yellow_diamond}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_square, green_star), (green_hexagon, purple_hexagon), (green_triangle, yellow_diamond)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell019_seed00019002","image":"images/path_test_cell019_seed00019002.png","image_sha256":"98f8ef35455209ecff06059e84ae2839af83d6cb3f07dfe6aced7ca86be1cb4a","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, green_diamond, purple_square, purple_star, yellow_circle, yellow_square}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, purple_square), (green_diamond, yellow_circle), (purple_star, yellow_square)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell019_seed00019003","image":"images/path_test_cell019_seed00019003.png","image_sha256":"f2182860f228305499a7c0a12b7dfb093592d0045e85c3a5198f96c1d0a668e0","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_triangle, green_hexagon, green_triangle, orange_star, purple_diamond, red_circle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_triangle, orange_star), (green_hexagon, green_triangle), (purple_diamond, red_circle)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell019_seed00019004","image":"images/path_test_cell019_seed00019004.png","image_sha256":"08d8152c450879d56f0ed2e0704e6b6229a6447fa23ffab5e35f3416bcecd6f8","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {green_circle, green_diamond, orange_square, purple_square, red_star, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(green_circle, purple_square), (green_diamond, orange_square), (red_star, yellow_star)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell020_seed00020000","image":"images/path_test_cell020_seed00020000.png","image_sha256":"bb8a4585ab38e773cb793a2679684542a3a265879d9d4ebf3680f0597b86eb35","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {green_hexagon, green_square, orange_diamond, red_square, red_triangle, yellow_square}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(green_hexagon, green_square), (orange_diamond, yellow_square), (red_square, red_triangle)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell020_seed00020001","image":"images/path_test_cell020_seed00020001.png","image_sha256":"f34cdd0d7d822ced32cb86b7297d347a61bbb81407d46e7099f15805ade27ea6","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {orange_diamond, orange_triangle, red_circle, red_hexagon, red_star, yellow_square}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(orange_diamond, red_hexagon), (orange_triangle, red_circle), (red_star, yellow_square)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell020_seed00020002","image":"images/path_test_cell020_seed00020002.png","image_sha256":"05483bf1e7f3c502fe7dca8ecaa7164cd6e6637b10abd0fec998a0bb2b6d19cc","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, green_square, green_triangle, orange_circle, purple_triangle, yellow_diamond}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, green_square), (green_triangle, yellow_diamond), (orange_circle, purple_triangle)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell020_seed00020003","image":"images/path_test_cell020_seed00020003.png","image_sha256":"2111c7aa2f1cd80be014c9b9c5fa937330489aa316b13c25cbbf3738ff7d9548","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_triangle, orange_square, orange_star, purple_star, red_hexagon, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_triangle, yellow_star), (orange_square, red_hexagon), (orange_star, purple_star)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell020_seed00020004","image":"images/path_test_cell020_seed00020004.png","image_sha256":"e819fac34895a1aead78a9c1ddabb437dcf1a7ca1c975de69094126417d28c55","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, blue_hexagon, blue_square, purple_hexagon, red_hexagon, yellow_circle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, red_hexagon), (blue_hexagon, purple_hexagon), (blue_square, yellow_circle)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell021_seed00021000","image":"images/path_test_cell021_seed00021000.png","image_sha256":"bd5ff7f9eb6890f49b54b3f30cf59640eb715889b11f5d42ece210a5e971fb4a","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_hexagon, green_circle, purple_triangle, red_diamond, yellow_diamond, yellow_hexagon}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_hexagon, purple_triangle), (green_circle, yellow_diamond), (red_diamond, yellow_hexagon)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell021_seed00021001","image":"images/path_test_cell021_seed00021001.png","image_sha256":"be35c173a14d6cb861f39f431884bc84ac05063529d3d659f97a727fc04c01da","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, orange_square, purple_circle, yellow_diamond, yellow_star, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, yellow_triangle), (orange_square, yellow_diamond), (purple_circle, yellow_star)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell021_seed00021002","image":"images/path_test_cell021_seed00021002.png","image_sha256":"dd5a11419f37dd826f39d5bba73a9fc2f2ba86dcbbff172ba589e23cd9a27cd5","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, orange_circle, purple_square, red_square, yellow_hexagon, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, yellow_hexagon), (orange_circle, yellow_triangle), (purple_square, red_square)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell021_seed00021003","image":"images/path_test_cell021_seed00021003.png","image_sha256":"0aeef0c8632e9cc5f77c93d0db8ea2e72e1b6b57250bffe41b10661dd1363f88","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {green_square, green_star, orange_diamond, orange_triangle, red_square, red_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(green_square, green_star), (orange_diamond, red_square), (orange_triangle, red_triangle)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell021_seed00021004","image":"images/path_test_cell021_seed00021004.png","image_sha256":"12db138cf85f7d3464a5200979d97fbdcd0ac48e46ffa14a889ed1943289fd39","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_diamond, green_hexagon, orange_square, red_triangle, yellow_circle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, red_triangle), (blue_diamond, orange_square), (green_hexagon, yellow_circle)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell022_seed00022000","image":"images/path_test_cell022_seed00022000.png","image_sha256":"9c5d3bb9edd71496b0431241c18fce9cf87961de6eaf04007938fbf896c42f2c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {orange_diamond, orange_star, purple_diamond, yellow_circle, yellow_hexagon, yellow_square}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(orange_diamond, yellow_hexagon), (orange_star, purple_diamond), (yellow_circle, yellow_square)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell022_seed00022001","image":"images/path_test_cell022_seed00022001.png","image_sha256":"a042578d3533eae1c0320312487d0039c5b4cbb0974fbb91dc211f9aa251de40","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_diamond, green_circle, orange_triangle, yellow_circle, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, green_circle), (blue_diamond, yellow_triangle), (orange_triangle, yellow_circle)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell022_seed00022002","image":"images/path_test_cell022_seed00022002.png","image_sha256":"0f63666e101f5c337c89a30b1458ad80b5b950072daafbf05ea21938cff670e4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {green_square, orange_square, red_diamond, red_triangle, yellow_circle, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(green_square, yellow_star), (orange_square, red_triangle), (red_diamond, yellow_circle)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell022_seed00022003","image":"images/path_test_cell022_seed00022003.png","image_sha256":"580984d7cc06a0aa34a850af3b1df6d68df19e85ee1f208cda41c164a9de0fc3","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, green_square, orange_diamond, orange_square, purple_circle, red_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, red_star), (green_square, purple_circle), (orange_diamond, orange_square)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell022_seed00022004","image":"images/path_test_cell022_seed00022004.png","image_sha256":"3c12239438e78022d21734e558cd301ec89e02966797b0f4a17fefc02204c4d3","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {green_hexagon, green_star, orange_hexagon, purple_square, red_circle, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(green_hexagon, green_star), (orange_hexagon, yellow_star), (purple_square, red_circle)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell023_seed00023000","image":"images/path_test_cell023_seed00023000.png","image_sha256":"7a5b42e6869d312a39ca6150ab721250c1506b83a1942a464951dc444123693c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_diamond, blue_star, orange_star, yellow_diamond, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, yellow_diamond), (blue_diamond, yellow_triangle), (blue_star, orange_star)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell023_seed00023001","image":"images/path_test_cell023_seed00023001.png","image_sha256":"5ff03ce538f90539df04db4ccafc738c28b914c0dc7245bcb67f9e2efb24ddd4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_hexagon, blue_triangle, green_star, orange_star, red_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, blue_hexagon), (blue_triangle, orange_star), (green_star, red_star)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell023_seed00023002","image":"images/path_test_cell023_seed00023002.png","image_sha256":"4a4623dee4e8afa8ff5884a01b194ab4ede0f78ab4aeef80ef24fefc3fe5ee09","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_triangle, purple_circle, purple_diamond, yellow_hexagon, yellow_star, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_triangle, yellow_hexagon), (purple_circle, yellow_star), (purple_diamond, yellow_triangle)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell023_seed00023003","image":"images/path_test_cell023_seed00023003.png","image_sha256":"0b7bafd21afc4d59fdd1c74434323a81c51f465e6887375b4022b79acfaed652","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, purple_diamond, purple_triangle, red_hexagon, red_triangle, yellow_circle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, red_triangle), (purple_diamond, red_hexagon), (purple_triangle, yellow_circle)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell023_seed00023004","image":"images/path_test_cell023_seed00023004.png","image_sha256":"f156f0fbcf9321eaa6da1505d1dd7c6aa76c7abcd0155a59e9b34727d78213f4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_triangle, green_circle, green_triangle, orange_diamond, orange_square, purple_hexagon}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_triangle, orange_square), (green_circle, orange_diamond), (green_triangle, purple_hexagon)}.","difficulty":"easy","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell024_seed00024000","image":"images/path_test_cell024_seed00024000.png","image_sha256":"f37f70bcb0a7f114556f2322528f3845aff39acf790f74acfd0bacbec178f4b2","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {E, J, O, P, S, W, X, Y}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(E, X), (J, W), (O, P), (S, Y)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell024_seed00024001","image":"images/path_test_cell024_seed00024001.png","image_sha256":"0bc0fd5a2ba9e354e1eb730937b0cbd21860622484b097f5cd446a8b079917ad","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, C, D, R, V, W, Y, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, R), (C, Y), (D, W), (V, Z)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell024_seed00024002","image":"images/path_test_cell024_seed00024002.png","image_sha256":"8fa583607c62db0d4ae5136699eb7fd6c1c00f42b883dc3e76623fa7c200ad27","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, C, F, K, N, P, R, Y}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, Y), (C, K), (F, R), (N, P)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell024_seed00024003","image":"images/path_test_cell024_seed00024003.png","image_sha256":"07830b0b50e16c7b956f8c9f4d1e386a9bd974552d2311796b2cdc1c344f5b99","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {C, F, K, L, P, Q, R, U, W, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(C, U), (F, W), (K, P), (L, Z), (Q, R)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell024_seed00024004","image":"images/path_test_cell024_seed00024004.png","image_sha256":"c42308a7faf691a435c0340a17725fd352062f96736b47d91826b39f9da57cef","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, C, D, E, G, I, Q, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, C), (D, E), (G, I), (Q, Z)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell025_seed00025000","image":"images/path_test_cell025_seed00025000.png","image_sha256":"61fc6736167b1e9aec87ef29453ed7ea6eecf09e30a4b47f36e8fd510b7ecf6d","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, B, C, E, I, J, K, S, V, W}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, C), (B, S), (E, V), (I, K), (J, W)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell025_seed00025001","image":"images/path_test_cell025_seed00025001.png","image_sha256":"00fb8f14a559d55c9053690699a2ce02231de8481bb9ca7a4db2d67d35893a21","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {E, G, J, K, L, P, R, T, V, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(E, J), (G, P), (K, R), (L, T), (V, Z)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell025_seed00025002","image":"images/path_test_cell025_seed00025002.png","image_sha256":"4e4831a66570513f97de163135ee0406d344e526cea166fce900a310531460a1","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, E, F, I, J, K, P, S, W, Y}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, W), (E, I), (F, J), (K, Y), (P, S)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell025_seed00025003","image":"images/path_test_cell025_seed00025003.png","image_sha256":"564a495ea6585beecbd0bc10bb044416704a8d83a6975136dde38e0d33f4c697","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, C, E, H, J, N, P, W, X, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, C), (E, X), (H, J), (N, W), (P, Z)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell025_seed00025004","image":"images/path_test_cell025_seed00025004.png","image_sha256":"2b490b3d12e2a45b643c1dad9888b1f02ae21df883cbc7ee09b8448f70225b98","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, D, G, I, N, R, S, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, R), (D, G), (I, S), (N, Z)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell026_seed00026000","image":"images/path_test_cell026_seed00026000.png","image_sha256":"9b7106ec6ca9fce9a2eb09645ce1447f78b6cff6fc9ca8339e23a8b280ea419f","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {C, D, G, I, K, L, N, P, Q, U}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(C, Q), (D, K), (G, I), (L, N), (P, U)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell026_seed00026001","image":"images/path_test_cell026_seed00026001.png","image_sha256":"49d00ea71ba95598c65aa9944f47afc87d349eea6de0acec84af0ac7458093cd","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, D, F, H, M, O, R, U, X, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, Z), (D, M), (F, O), (H, R), (U, X)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell026_seed00026002","image":"images/path_test_cell026_seed00026002.png","image_sha256":"134db0c3f2af9b727d02edaf2ef67336d766edc5a3776ca8069bb450953bf673","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {H, I, L, P, Q, S, T, U, W, Y}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(H, P), (I, W), (L, S), (Q, U), (T, Y)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell026_seed00026003","image":"images/path_test_cell026_seed00026003.png","image_sha256":"66782b8ef299d2f42f96f1329091679a3dec6861113e9e6234f54d43722fced6","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {C, D, E, H, I, K, N, O, Q, Y}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(C, I), (D, O), (E, N), (H, K), (Q, Y)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell026_seed00026004","image":"images/path_test_cell026_seed00026004.png","image_sha256":"b2d429eb09d7b8c82996901e668ee37791cc99e633330e2d1c5b9c62c84a3f33","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {D, F, G, L, M, P, Q, W}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(D, L), (F, G), (M, P), (Q, W)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell027_seed00027000","image":"images/path_test_cell027_seed00027000.png","image_sha256":"0a41fb99af3aaeee1e53e2795dba61907857eb5aaa4216a93ba68c2252b3e9d7","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, F, I, J, K, M, P, U, X, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, U), (F, P), (I, M), (J, K), (X, Z)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell027_seed00027001","image":"images/path_test_cell027_seed00027001.png","image_sha256":"0075dcbe68a169bb1bf35507bb52e06013233e923355022b60098c7a5df58c49","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {C, D, G, H, J, M, O, Q, V, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(C, G), (D, O), (H, V), (J, M), (Q, Z)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell027_seed00027002","image":"images/path_test_cell027_seed00027002.png","image_sha256":"5d0c25d14795425a9c5278b06c5bbd928006dddcefe9a05a8262741b926ac43b","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, C, G, I, K, N, Q, U, W, Y}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, N), (C, K), (G, W), (I, U), (Q, Y)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell027_seed00027003","image":"images/path_test_cell027_seed00027003.png","image_sha256":"1d499defb7a1a908b6e1c436056cc06e62637e4bcdbfcd971b0761eff736e452","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {C, F, G, I, P, S, X, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(C, G), (F, S), (I, P), (X, Z)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell027_seed00027004","image":"images/path_test_cell027_seed00027004.png","image_sha256":"9213e24ef43855decf05f42e472c736fe164f5e6cbc53b53d79dae9055587e94","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {C, D, I, K, L, M, R, T, W, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(C, Z), (D, T), (I, R), (K, L), (M, W)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell028_seed00028000","image":"images/path_test_cell028_seed00028000.png","image_sha256":"f8507f795b888282d5830ad1cc44bb86edca44701976db8437ab649e3c0d1bf2","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {F, J, P, Q, U, V, W, X}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(F, Q), (J, P), (U, W), (V, X)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell028_seed00028001","image":"images/path_test_cell028_seed00028001.png","image_sha256":"528507bf3cdd4f7a4b7aef3444b00d7c194926f429160bcdf189874223514589","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, H, J, M, O, T, X, Y}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, X), (H, Y), (J, T), (M, O)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell028_seed00028002","image":"images/path_test_cell028_seed00028002.png","image_sha256":"daa1f5f74a755b7fa931efbb0763203257a72f81bf2c4aefa701001f01db23b0","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {C, E, H, J, K, L, S, U, V, W}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(C, V), (E, J), (H, K), (L, U), (S, W)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell028_seed00028003","image":"images/path_test_cell028_seed00028003.png","image_sha256":"11b6e578a952af1b92d1941d38ccfc2463802f1dbbc40b36afefc1fa387de990","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, B, C, K, L, Q, R, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, R), (B, C), (K, Z), (L, Q)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell028_seed00028004","image":"images/path_test_cell028_seed00028004.png","image_sha256":"0c1a7192c7b30a231842a21a5fc8497377c0ee9dc3c9845cd8524d3bcb2bcd52","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {C, D, E, G, K, M, N, O, R, S}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(C, M), (D, S), (E, R), (G, N), (K, O)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell029_seed00029000","image":"images/path_test_cell029_seed00029000.png","image_sha256":"a6cd611fb9239a1ea53a86cd88328306aa162ce5b6cd6b9ac9596cb023c932fd","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, C, D, E, M, P, R, W}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, C), (D, P), (E, W), (M, R)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell029_seed00029001","image":"images/path_test_cell029_seed00029001.png","image_sha256":"c2fb34e0e7ab824b9d4f8eaf9600d2b8e8a09abe1f33eac9f49a37c6d1501db2","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, D, E, G, J, L, M, O, Q, X}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, M), (D, X), (E, Q), (G, L), (J, O)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell029_seed00029002","image":"images/path_test_cell029_seed00029002.png","image_sha256":"47021880816725c6a8c4baad962f600fe6924d5278f080301951d147e93ffdac","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, E, G, L, P, Q, U, Y}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, G), (E, L), (P, U), (Q, Y)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell029_seed00029003","image":"images/path_test_cell029_seed00029003.png","image_sha256":"6f9813227536289cd9acc41699aa60f393dfb535c12780cb3dc36ef22c1565dc","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, F, K, R, S, T, U, X, Y, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, X), (F, K), (R, U), (S, T), (Y, Z)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell029_seed00029004","image":"images/path_test_cell029_seed00029004.png","image_sha256":"86f74c078a324d3d51ac957b29b900cc31262259de2da267a750735f95db1614","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {D, F, H, J, N, Q, T, U, W, Y}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(D, H), (F, W), (J, N), (Q, U), (T, Y)}.","difficulty":"medium","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell030_seed00030000","image":"images/path_test_cell030_seed00030000.png","image_sha256":"bca084f2063045244bdc1c14cf9276ef4332d88b7c545610f4186b5c8a12aa0b","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {11, 18, 27, 28, 41, 59, 61, 72, 82, 92}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(11, 28), (18, 27), (41, 59), (61, 72), (82, 92)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell030_seed00030001","image":"images/path_test_cell030_seed00030001.png","image_sha256":"0046c362982c5705659d6f43fab0afd9b0b8710907b5d523f2c8fad1f2d350ae","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {9, 13, 17, 53, 80, 88, 90, 99}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(9, 53), (13, 80), (17, 99), (88, 90)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell030_seed00030002","image":"images/path_test_cell030_seed00030002.png","image_sha256":"71c50f8597f9fa86e3bf64ccd6ebbce46f125a6bc7e4d5a9d8288b2bfef1a721","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {16, 36, 41, 50, 60, 61, 89, 91}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(16, 89), (36, 50), (41, 91), (60, 61)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell030_seed00030003","image":"images/path_test_cell030_seed00030003.png","image_sha256":"c516fa287ea39a7a83296d90278653e901e0986d83e3227583d5ae6eb7e585e7","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {7, 8, 40, 41, 48, 50, 54, 69, 71, 95}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(7, 54), (8, 40), (41, 50), (48, 71), (69, 95)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell030_seed00030004","image":"images/path_test_cell030_seed00030004.png","image_sha256":"9f0daf4619c6589194add0d1f9ec45a1648b0ba05ee2f902f40cee387212b4ee","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {10, 16, 21, 60, 73, 81, 83, 85}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(10, 73), (16, 81), (21, 85), (60, 83)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell031_seed00031000","image":"images/path_test_cell031_seed00031000.png","image_sha256":"ebe75ea80e67079087bcd2d6b6402ca370b5046c11627ba57fb60b9a85f977cd","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {23, 27, 40, 52, 60, 68, 74, 96}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(23, 27), (40, 74), (52, 60), (68, 96)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell031_seed00031001","image":"images/path_test_cell031_seed00031001.png","image_sha256":"87869a92128ce69088d769dcb51ae6d2169d17494028ec2a3db9761d2516e2c2","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {31, 33, 35, 40, 41, 58, 76, 89, 92, 98}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(31, 58), (33, 92), (35, 89), (40, 76), (41, 98)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell031_seed00031002","image":"images/path_test_cell031_seed00031002.png","image_sha256":"424cae40f0bcd4c49df1fb4ac185a02312e14d2b8dfa2848ac426108279d7914","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {6, 9, 20, 43, 49, 56, 66, 69, 73, 75}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(6, 66), (9, 75), (20, 69), (43, 56), (49, 73)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell031_seed00031003","image":"images/path_test_cell031_seed00031003.png","image_sha256":"85a444cd714c3dc091d0d6f404e8f9c99f936e470adbb3099d72878561adeb64","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {5, 13, 24, 36, 42, 48, 65, 67, 72, 78}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(5, 13), (24, 67), (36, 65), (42, 48), (72, 78)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell031_seed00031004","image":"images/path_test_cell031_seed00031004.png","image_sha256":"bcb92347ba43bc12d854f2ac29756f4bb53d7164c65180dc3960589b3edfffec","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {19, 23, 32, 41, 51, 67, 68, 80}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(19, 80), (23, 51), (32, 67), (41, 68)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell032_seed00032000","image":"images/path_test_cell032_seed00032000.png","image_sha256":"fa492b19092a89c53dfa253ff513d6e9961b7e0f80354ea7adfc3eb63ef7730c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {9, 17, 20, 29, 30, 52, 68, 78, 86, 95}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(9, 95), (17, 30), (20, 86), (29, 52), (68, 78)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell032_seed00032001","image":"images/path_test_cell032_seed00032001.png","image_sha256":"27544258842e8a3f0a998f39f14ce6f42ffa334ff6399b1d1d2dcc4afe9777c4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {16, 24, 42, 49, 62, 63, 88, 95}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(16, 42), (24, 88), (49, 62), (63, 95)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell032_seed00032002","image":"images/path_test_cell032_seed00032002.png","image_sha256":"3ef57b400e2ce6b00ba5d3b27706a64cd4356485ecebfd88aaa5eafcc38b8bf1","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {15, 38, 39, 42, 60, 74, 75, 90}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(15, 60), (38, 90), (39, 75), (42, 74)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell032_seed00032003","image":"images/path_test_cell032_seed00032003.png","image_sha256":"45734a216adba59ffed1caa457da974e55e36c10a86018bd1513dd71708d61f4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {19, 37, 42, 45, 55, 64, 82, 88}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(19, 45), (37, 64), (42, 82), (55, 88)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell032_seed00032004","image":"images/path_test_cell032_seed00032004.png","image_sha256":"113d478f68ed18182435ae599719c9a75d76e78549001bcc047e9bd8b1f6c122","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {3, 13, 25, 37, 70, 72, 93, 98}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(3, 72), (13, 25), (37, 70), (93, 98)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell033_seed00033000","image":"images/path_test_cell033_seed00033000.png","image_sha256":"1124093dbafed44b7f32813edf15070c798719eec49057d26ae58d3524e3d727","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {9, 13, 20, 21, 23, 28, 29, 33, 70, 72}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(9, 70), (13, 20), (21, 23), (28, 29), (33, 72)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell033_seed00033001","image":"images/path_test_cell033_seed00033001.png","image_sha256":"2f8caa806f6aad89fc6f807c57de07c833e0189698613eddce2f9391567d9e4c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {2, 31, 34, 39, 49, 74, 79, 85, 97, 99}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(2, 99), (31, 85), (34, 97), (39, 49), (74, 79)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell033_seed00033002","image":"images/path_test_cell033_seed00033002.png","image_sha256":"14c79215f889c2d21d11e3cbfcf99bf6532d157273cc02c5ebc4b7a080746db0","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {1, 24, 27, 32, 34, 49, 55, 72, 75, 97}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(1, 27), (24, 75), (32, 49), (34, 72), (55, 97)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell033_seed00033003","image":"images/path_test_cell033_seed00033003.png","image_sha256":"e234c6635d7007888445052f9cb52805c182e0b72eac7d5ecfc16406a2cc7d24","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {28, 33, 34, 40, 53, 62, 82, 90}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(28, 53), (33, 90), (34, 62), (40, 82)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell033_seed00033004","image":"images/path_test_cell033_seed00033004.png","image_sha256":"fc76cc57193187790771c16a3de5f56d898be4676866e123dee7c2b4a8f1a2ac","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {24, 34, 35, 42, 50, 57, 63, 82}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(24, 63), (34, 82), (35, 50), (42, 57)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell034_seed00034000","image":"images/path_test_cell034_seed00034000.png","image_sha256":"53021128e6e600c5e011bc8a3b5aa79d95d081905de9429992898251af84ca92","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {9, 10, 24, 43, 52, 73, 75, 93}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(9, 43), (10, 75), (24, 52), (73, 93)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell034_seed00034001","image":"images/path_test_cell034_seed00034001.png","image_sha256":"7b438a7fdb78ceb622c4e99f3b00fdfdef28e5955b9a40279555dddc00abe7f8","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {25, 35, 55, 64, 68, 80, 82, 90}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(25, 64), (35, 80), (55, 82), (68, 90)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell034_seed00034002","image":"images/path_test_cell034_seed00034002.png","image_sha256":"acc2b9e83df383dccf7a6fb8f8baee035f6e35c046aa885ef794626af9dc0468","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {43, 52, 64, 78, 79, 86, 92, 93}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(43, 64), (52, 78), (79, 86), (92, 93)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell034_seed00034003","image":"images/path_test_cell034_seed00034003.png","image_sha256":"ad678007de1b50790741c31b0eed6d6edd2502c0a422b94c37d447a925308ce8","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {6, 12, 19, 30, 31, 59, 64, 71, 84, 94}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(6, 12), (19, 30), (31, 84), (59, 94), (64, 71)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell034_seed00034004","image":"images/path_test_cell034_seed00034004.png","image_sha256":"eb2fa36ff2bbc8a939df65631df2652b08437e35eea37441f6025b1d20a36a4c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {7, 22, 43, 70, 77, 85, 95, 99}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(7, 43), (22, 99), (70, 77), (85, 95)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell035_seed00035000","image":"images/path_test_cell035_seed00035000.png","image_sha256":"7f9d0d801c1608365b328a851c2269ed7021e1b34a3a64ce4906faf5ef2ce2f5","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {2, 6, 24, 36, 49, 57, 73, 80}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(2, 73), (6, 57), (24, 36), (49, 80)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell035_seed00035001","image":"images/path_test_cell035_seed00035001.png","image_sha256":"3a9e2c2f39a501ee6455718cdeb880c369f60facda3ca459b7f79b32effc83e4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {3, 17, 54, 60, 70, 78, 81, 92}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(3, 17), (54, 78), (60, 81), (70, 92)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell035_seed00035002","image":"images/path_test_cell035_seed00035002.png","image_sha256":"6939ab2465b598d212ff2e6f9d64f2635d812b324349d8a40f07cf46b8d5d92c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {21, 27, 28, 30, 39, 56, 74, 89}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(21, 27), (28, 74), (30, 56), (39, 89)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell035_seed00035003","image":"images/path_test_cell035_seed00035003.png","image_sha256":"f5d6161ea7291796cf9ff2a1d06739e416b51840d76401e9335b009a80a17671","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {10, 16, 20, 26, 46, 51, 66, 88}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(10, 66), (16, 88), (20, 46), (26, 51)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell035_seed00035004","image":"images/path_test_cell035_seed00035004.png","image_sha256":"9134321f81a9fcf848360eb23bafd2c8910acffcd01a2fb66c8382c78120b7f2","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {3, 4, 27, 28, 30, 32, 77, 88}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(3, 28), (4, 32), (27, 88), (30, 77)}.","difficulty":"medium","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell036_seed00036000","image":"images/path_test_cell036_seed00036000.png","image_sha256":"a40dd12176ed961e3da85e6882422744b3d41940b7a7032358576d5bd690c17a","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {butterfly, cloud, dog, fish, hammer, key, lock, mushroom}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(butterfly, mushroom), (cloud, lock), (dog, fish), (hammer, key)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell036_seed00036001","image":"images/path_test_cell036_seed00036001.png","image_sha256":"2b1bc91ed3016b01acddb6e6c8e6c6919cbfdf9705cb482fd64d8531de4836d6","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {apple, carrot, crown, diamond_shape, dog, gift, lightning, lock, pizza, rocket}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(apple, crown), (carrot, rocket), (diamond_shape, lock), (dog, gift), (lightning, pizza)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell036_seed00036002","image":"images/path_test_cell036_seed00036002.png","image_sha256":"c9fbf9997c0fb5c375f4bd8b01a8b4135811b8606e9192d192007d2e6881d3b8","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, carrot, cookie, diamond_shape, dog, heart, music_note, owl, pizza, rocket}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, pizza), (carrot, owl), (cookie, music_note), (diamond_shape, heart), (dog, rocket)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell036_seed00036003","image":"images/path_test_cell036_seed00036003.png","image_sha256":"ad064c85ce01fc019d01fbf43e847be5b35211bbebd96e08d174aeabcd9e7955","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {apple, butterfly, cloud, cookie, diamond_shape, heart, key, music_note, pizza, star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(apple, heart), (butterfly, key), (cloud, cookie), (diamond_shape, music_note), (pizza, star)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell036_seed00036004","image":"images/path_test_cell036_seed00036004.png","image_sha256":"c2afa36d01f49774ec8ef1e642fa96f27d63d74a66bd0423337b9157e1bbfc74","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {balloon, banana, carrot, cloud, crown, diamond_shape, fire, rocket, scissors, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(balloon, carrot), (banana, fire), (cloud, crown), (diamond_shape, rocket), (scissors, sun)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell037_seed00037000","image":"images/path_test_cell037_seed00037000.png","image_sha256":"7ed516f8391d2c1a6651da914c00451b18e58e40ff2f18e748b05739ece33f16","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, balloon, cookie, hammer, magnet, music_note, octopus, owl}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, magnet), (balloon, cookie), (hammer, owl), (music_note, octopus)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell037_seed00037001","image":"images/path_test_cell037_seed00037001.png","image_sha256":"0af8598e63203efe0bde44cfc9e2ba3368daf5dd217892fb2a41d2028e0ce3a3","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {cat, cookie, diamond_shape, hammer, key, lightning, octopus, snake, star, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(cat, sun), (cookie, snake), (diamond_shape, star), (hammer, octopus), (key, lightning)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell037_seed00037002","image":"images/path_test_cell037_seed00037002.png","image_sha256":"f387e5fe10c1a91ec64f071e406dba0710cfcf9adeaef06c17deaa2b21dc6889","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {balloon, banana, crown, hammer, heart, rocket, snake, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(balloon, hammer), (banana, rocket), (crown, sun), (heart, snake)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell037_seed00037003","image":"images/path_test_cell037_seed00037003.png","image_sha256":"898e0dff36a07480be08cf7e08923ea728490e97342c7ca21db25b7ed653bc8b","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {apple, balloon, butterfly, fire, flower, heart, music_note, rocket}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(apple, rocket), (balloon, heart), (butterfly, flower), (fire, music_note)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell037_seed00037004","image":"images/path_test_cell037_seed00037004.png","image_sha256":"530a736af1670fbfc2529b2f48bec053b843b4b33d09dfb707c0ae493a638301","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, butterfly, diamond_shape, fish, heart, magnet, music_note, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, sun), (butterfly, magnet), (diamond_shape, fish), (heart, music_note)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell038_seed00038000","image":"images/path_test_cell038_seed00038000.png","image_sha256":"13fff2e3996e265766aa82d95c9315670964dde1780c8fa09cfb87ce55b65a45","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {apple, banana, blue_circle, cake, flower, gift, heart, pizza, rocket, snake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(apple, flower), (banana, blue_circle), (cake, rocket), (gift, snake), (heart, pizza)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell038_seed00038001","image":"images/path_test_cell038_seed00038001.png","image_sha256":"b50fb837a627ff80a588b1b24f3b5f86f66dbbd0219e750ce354a4835fc12f2f","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, butterfly, cat, cloud, cookie, crown, key, mushroom, music_note, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, key), (butterfly, music_note), (cat, sun), (cloud, mushroom), (cookie, crown)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell038_seed00038002","image":"images/path_test_cell038_seed00038002.png","image_sha256":"62901bcb041a1abe2480b0d357d5d77fceff33d4edbf3d43aa2aece9c7900186","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, carrot, cloud, fire, flower, magnet, owl, pizza}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, cloud), (carrot, pizza), (fire, magnet), (flower, owl)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell038_seed00038003","image":"images/path_test_cell038_seed00038003.png","image_sha256":"c4a1eedb2a7dba7e38e029520301b89b9ab3826101a2e857295f0875776b4bd0","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, balloon, blue_circle, cookie, crown, light_bulb, lightning, magnet}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, balloon), (blue_circle, cookie), (crown, magnet), (light_bulb, lightning)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell038_seed00038004","image":"images/path_test_cell038_seed00038004.png","image_sha256":"710b6cd3d9344de810a5edee3bd0c408f443eb09fbb2080cd262d458d74854b1","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, balloon, cake, cookie, fish, light_bulb, moon, scissors, snake, snowflake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, snowflake), (balloon, snake), (cake, light_bulb), (cookie, scissors), (fish, moon)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell039_seed00039000","image":"images/path_test_cell039_seed00039000.png","image_sha256":"17625e2948d8e7714040a139491df4337aec9f112497f16fe57d7021048f56da","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, apple, balloon, crown, diamond_shape, dog, gift, moon, mushroom, music_note}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, music_note), (apple, mushroom), (balloon, dog), (crown, moon), (diamond_shape, gift)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell039_seed00039001","image":"images/path_test_cell039_seed00039001.png","image_sha256":"6f8fb21d13e4e9dbe217aa222af57f2edf3bae1b18fe69d67c42c1aa4985bb44","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {butterfly, carrot, dog, gift, hammer, music_note, octopus, pizza, scissors, star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(butterfly, music_note), (carrot, hammer), (dog, pizza), (gift, octopus), (scissors, star)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell039_seed00039002","image":"images/path_test_cell039_seed00039002.png","image_sha256":"4d155ce2079ca853340f8209f21215b7bb67c7d6793887f1250efeb5c8c3631d","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, apple, butterfly, cloud, key, light_bulb, moon, mushroom, rocket, scissors}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, moon), (apple, cloud), (butterfly, light_bulb), (key, mushroom), (rocket, scissors)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell039_seed00039003","image":"images/path_test_cell039_seed00039003.png","image_sha256":"b88d3b5120354da29fde2729df4c93b49214c0df24faa10617b9ee3547e4f953","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {banana, carrot, cookie, dog, lightning, mushroom, pizza, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(banana, mushroom), (carrot, cookie), (dog, pizza), (lightning, sun)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell039_seed00039004","image":"images/path_test_cell039_seed00039004.png","image_sha256":"52cc31acc6c006778fa2c68389485345d547f0cf5cf7f86a7a24f34b1db1634a","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {banana, blue_circle, diamond_shape, fire, lightning, octopus, pizza, star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(banana, fire), (blue_circle, lightning), (diamond_shape, star), (octopus, pizza)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell040_seed00040000","image":"images/path_test_cell040_seed00040000.png","image_sha256":"a375e20bbe4d77af04260bb358c53340fae0c0d6c16c8520971b9f44cf99808c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {banana, blue_circle, cloud, crown, dog, flower, hammer, scissors, star, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(banana, cloud), (blue_circle, scissors), (crown, sun), (dog, star), (flower, hammer)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell040_seed00040001","image":"images/path_test_cell040_seed00040001.png","image_sha256":"285cc608a589a87310cf88fda90f4bb770c576f36509b68ec7c31767022f2bca","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {balloon, cat, cloud, fish, heart, owl, pizza, snowflake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(balloon, snowflake), (cat, fish), (cloud, pizza), (heart, owl)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell040_seed00040002","image":"images/path_test_cell040_seed00040002.png","image_sha256":"01232fb3da6a5a8c5c14cefab30284ff026297790a1bc020bba300d7eddd9aec","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {bee, cookie, fire, fish, hammer, key, mushroom, pizza}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(bee, mushroom), (cookie, hammer), (fire, pizza), (fish, key)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell040_seed00040003","image":"images/path_test_cell040_seed00040003.png","image_sha256":"8e4c998277e24b0f8c5a3e9357f47031f7fa4fa1d4b2d60e98e836717c730af5","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {balloon, banana, butterfly, cake, fish, heart, lock, music_note, pizza, snake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(balloon, fish), (banana, lock), (butterfly, pizza), (cake, music_note), (heart, snake)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell040_seed00040004","image":"images/path_test_cell040_seed00040004.png","image_sha256":"8ffbee0c9a39780f2d0079825a236c1390cff3d863a34002307b4490d7920e80","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, cat, crown, diamond_shape, dog, magnet, scissors, star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, scissors), (cat, magnet), (crown, diamond_shape), (dog, star)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell041_seed00041000","image":"images/path_test_cell041_seed00041000.png","image_sha256":"fcc811a2bd0297e3efc7b916025372f1c00af0cb92b2ff8c68ba59aa1434714a","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {balloon, blue_circle, cookie, music_note, owl, rocket, snowflake, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(balloon, blue_circle), (cookie, rocket), (music_note, owl), (snowflake, sun)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell041_seed00041001","image":"images/path_test_cell041_seed00041001.png","image_sha256":"b83f20f237d840d40cc3eddc8cac3cbcc52d90ab354ad11c9c5b0eca38c8a20f","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {balloon, cookie, dog, fire, frog, light_bulb, scissors, snowflake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(balloon, cookie), (dog, scissors), (fire, light_bulb), (frog, snowflake)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell041_seed00041002","image":"images/path_test_cell041_seed00041002.png","image_sha256":"3711b58d854c3e384491d04f1f3865d198d10ccebb4572601aaf059925d28e13","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, apple, blue_circle, cat, crown, dog, gift, hammer, lock, rocket}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, apple), (blue_circle, gift), (cat, lock), (crown, hammer), (dog, rocket)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell041_seed00041003","image":"images/path_test_cell041_seed00041003.png","image_sha256":"d27d900c14a19864490a2dd9beab03e495e88576351ea7603ccc9c91bc2fa271","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, butterfly, carrot, cookie, diamond_shape, fire, lightning, lock, moon, snake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, snake), (butterfly, fire), (carrot, cookie), (diamond_shape, lightning), (lock, moon)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell041_seed00041004","image":"images/path_test_cell041_seed00041004.png","image_sha256":"0a07150eee347c477120e30050e180191fcc4d589887d39c6c9cb44cc7ed5e1f","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {bee, cake, cat, cloud, gift, key, scissors, snake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(bee, key), (cake, scissors), (cat, gift), (cloud, snake)}.","difficulty":"medium","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell042_seed00042000","image":"images/path_test_cell042_seed00042000.png","image_sha256":"a4df9193fcb996e24a4eb5874bfbecceded441648dd6079fef25d86c22b9f537","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_hexagon, blue_square, green_hexagon, orange_circle, orange_diamond, orange_star, purple_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, green_hexagon), (blue_hexagon, blue_square), (orange_circle, orange_star), (orange_diamond, purple_star)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell042_seed00042001","image":"images/path_test_cell042_seed00042001.png","image_sha256":"585c746496f7e4476ae2f36e5fc626bad98db5f97ae999c733f66dc8e66d31cc","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_square, blue_star, green_diamond, green_hexagon, green_square, green_star, purple_circle, red_hexagon, red_triangle, yellow_hexagon}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_square, yellow_hexagon), (blue_star, green_diamond), (green_hexagon, green_square), (green_star, red_hexagon), (purple_circle, red_triangle)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell042_seed00042002","image":"images/path_test_cell042_seed00042002.png","image_sha256":"8d48c270a39aef6362c69c270fc3e0438962e1cad83a1375e910b5363ebc95f4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, blue_square, green_diamond, orange_triangle, red_hexagon, red_star, yellow_circle, yellow_hexagon}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, blue_square), (green_diamond, red_star), (orange_triangle, red_hexagon), (yellow_circle, yellow_hexagon)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell042_seed00042003","image":"images/path_test_cell042_seed00042003.png","image_sha256":"ee899e335a280e881f0d0921252599c1737601a859a2842f28b96d588dad4d4d","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, blue_star, green_star, purple_star, red_hexagon, red_star, yellow_diamond, yellow_square}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, yellow_square), (blue_star, red_hexagon), (green_star, red_star), (purple_star, yellow_diamond)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell042_seed00042004","image":"images/path_test_cell042_seed00042004.png","image_sha256":"e4708f245efc5ade3e44a3e3d7f11fd69134cde71dde2fce605a991da680ba4f","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_square, blue_star, green_circle, orange_hexagon, purple_circle, purple_hexagon, purple_triangle, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_square, purple_circle), (blue_star, yellow_star), (green_circle, purple_triangle), (orange_hexagon, purple_hexagon)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell043_seed00043000","image":"images/path_test_cell043_seed00043000.png","image_sha256":"ba278d189608e9941bdfddf2fd4f4990ec7861bf07280d9c8b55e40cba4f0918","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {green_diamond, green_hexagon, orange_circle, orange_star, purple_diamond, purple_triangle, red_circle, red_hexagon}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(green_diamond, green_hexagon), (orange_circle, purple_diamond), (orange_star, purple_triangle), (red_circle, red_hexagon)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell043_seed00043001","image":"images/path_test_cell043_seed00043001.png","image_sha256":"10ddd99f6fa07349ccaf1b82cf71560a653885b890050941e52a6652c2ad33a3","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, green_square, orange_diamond, orange_star, purple_square, purple_star, purple_triangle, red_diamond, red_triangle, yellow_square}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, purple_triangle), (green_square, red_diamond), (orange_diamond, purple_square), (orange_star, red_triangle), (purple_star, yellow_square)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell043_seed00043002","image":"images/path_test_cell043_seed00043002.png","image_sha256":"c9cf6323c6f5e0226b267fe95700a205eda4f052573d835bdd66481c2f30fd75","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {green_diamond, green_hexagon, orange_star, orange_triangle, purple_triangle, red_diamond, yellow_hexagon, yellow_square}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(green_diamond, orange_star), (green_hexagon, yellow_hexagon), (orange_triangle, yellow_square), (purple_triangle, red_diamond)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell043_seed00043003","image":"images/path_test_cell043_seed00043003.png","image_sha256":"1612b62c3fd9b75005d8b6e6fd136eaa4fa06ab9b25e13f6c62e95453df6de60","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, blue_triangle, green_square, purple_circle, purple_star, yellow_circle, yellow_diamond, yellow_square}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, purple_circle), (blue_triangle, purple_star), (green_square, yellow_diamond), (yellow_circle, yellow_square)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell043_seed00043004","image":"images/path_test_cell043_seed00043004.png","image_sha256":"de92aae6e4dccdd95371fea9ec3730ba51a36c2cd887a3dc060655da6bfc38cb","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_star, green_hexagon, green_star, orange_diamond, purple_square, purple_triangle, red_circle, yellow_circle, yellow_square, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_star, purple_triangle), (green_hexagon, orange_diamond), (green_star, yellow_square), (purple_square, yellow_star), (red_circle, yellow_circle)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell044_seed00044000","image":"images/path_test_cell044_seed00044000.png","image_sha256":"93b16e0511dcfcb444ccf726e9f4ae39ea99aab3ea4c23958204de6cc8aa773f","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {green_circle, orange_circle, orange_star, purple_diamond, purple_square, red_triangle, yellow_hexagon, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(green_circle, orange_star), (orange_circle, purple_diamond), (purple_square, yellow_hexagon), (red_triangle, yellow_triangle)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell044_seed00044001","image":"images/path_test_cell044_seed00044001.png","image_sha256":"84ac4ab036df08f74c923a8c97b94bc2d5a5908dff439984fdea23822f9b61e3","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_triangle, orange_diamond, orange_star, orange_triangle, purple_square, red_circle, red_star, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_triangle, orange_star), (orange_diamond, red_circle), (orange_triangle, red_star), (purple_square, yellow_star)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell044_seed00044002","image":"images/path_test_cell044_seed00044002.png","image_sha256":"027e3dfce085b23e43a21f0faa6257070029091628915cf076c63fae21083ac0","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, green_hexagon, orange_hexagon, red_circle, red_diamond, red_star, red_triangle, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, red_circle), (green_hexagon, red_triangle), (orange_hexagon, yellow_star), (red_diamond, red_star)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell044_seed00044003","image":"images/path_test_cell044_seed00044003.png","image_sha256":"527d6bc44e66bf039d482fcc216594e265eb212bd222891f18a024184f1046c3","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_hexagon, blue_square, green_hexagon, green_triangle, orange_hexagon, orange_square, purple_triangle, yellow_diamond}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_hexagon, green_hexagon), (blue_square, orange_hexagon), (green_triangle, yellow_diamond), (orange_square, purple_triangle)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell044_seed00044004","image":"images/path_test_cell044_seed00044004.png","image_sha256":"9bac4c86bdd2164e0050a0807c12142569ccba7b357b9cf23c2b4684c775c50f","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_square, blue_triangle, purple_diamond, red_circle, red_square, yellow_circle, yellow_square, yellow_star, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, yellow_star), (blue_square, blue_triangle), (purple_diamond, yellow_circle), (red_circle, yellow_square), (red_square, yellow_triangle)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell045_seed00045000","image":"images/path_test_cell045_seed00045000.png","image_sha256":"aa802b00f987b50934d039dac26bf498657d8daec9117da06fdd699bc6dceaa5","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {orange_circle, orange_hexagon, orange_star, orange_triangle, red_diamond, red_triangle, yellow_circle, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(orange_circle, orange_star), (orange_hexagon, red_diamond), (orange_triangle, yellow_triangle), (red_triangle, yellow_circle)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell045_seed00045001","image":"images/path_test_cell045_seed00045001.png","image_sha256":"a560facc0aaa7cf3cd095ee4b658369d293d4837feb0bed5616b65681642503c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, orange_square, purple_diamond, red_hexagon, red_triangle, yellow_circle, yellow_diamond, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, yellow_diamond), (orange_square, yellow_triangle), (purple_diamond, yellow_circle), (red_hexagon, red_triangle)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell045_seed00045002","image":"images/path_test_cell045_seed00045002.png","image_sha256":"c861c554e8080c24f191f61d5ad74df7c2ca45916c407bda7d0a9163505a1193","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, blue_triangle, green_circle, green_diamond, purple_square, yellow_hexagon, yellow_star, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, green_circle), (blue_triangle, yellow_triangle), (green_diamond, yellow_star), (purple_square, yellow_hexagon)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell045_seed00045003","image":"images/path_test_cell045_seed00045003.png","image_sha256":"62fae53726a969bcec43c9945055f3acabea2d33375dd034f1302ca60caca870","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_star, green_diamond, orange_circle, orange_square, purple_diamond, red_diamond, red_hexagon, yellow_circle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_star, red_diamond), (green_diamond, yellow_circle), (orange_circle, orange_square), (purple_diamond, red_hexagon)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell045_seed00045004","image":"images/path_test_cell045_seed00045004.png","image_sha256":"65c7253b97fe7541e1f2c322ffbda6873836772266ca19edaac084c0c3cee44c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, blue_hexagon, blue_star, green_circle, green_square, purple_diamond, purple_square, red_triangle, yellow_circle, yellow_hexagon}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, green_square), (blue_hexagon, blue_star), (green_circle, yellow_hexagon), (purple_diamond, yellow_circle), (purple_square, red_triangle)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell046_seed00046000","image":"images/path_test_cell046_seed00046000.png","image_sha256":"12414512526fc0d958bd9f6a4c2c79490a502f0adf3d386ea3c27070c9b02f2b","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_square, blue_star, green_square, orange_hexagon, orange_triangle, purple_hexagon, red_square, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_square, purple_hexagon), (blue_star, orange_hexagon), (green_square, orange_triangle), (red_square, yellow_triangle)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell046_seed00046001","image":"images/path_test_cell046_seed00046001.png","image_sha256":"cb1f2ba5de8b5022c5bf2049f31e6c65cee2c66478477839fd5da6a5cebc5d32","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_star, green_square, green_triangle, orange_square, purple_square, red_hexagon, red_square, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_star, green_square), (green_triangle, orange_square), (purple_square, red_square), (red_hexagon, yellow_star)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell046_seed00046002","image":"images/path_test_cell046_seed00046002.png","image_sha256":"3f8755cba460cf8f61855a81eba307c5ef313bbb34144bf8941316f0db90e18f","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_triangle, green_triangle, orange_diamond, orange_star, orange_triangle, purple_diamond, purple_triangle, red_diamond, red_star, yellow_hexagon}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_triangle, red_diamond), (green_triangle, orange_diamond), (orange_star, red_star), (orange_triangle, purple_diamond), (purple_triangle, yellow_hexagon)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell046_seed00046003","image":"images/path_test_cell046_seed00046003.png","image_sha256":"9e16f2e7aae5371625870cb0dc68161a275eea6b8427ea94853f55d08634fe6d","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_star, green_diamond, green_hexagon, red_diamond, red_hexagon, yellow_circle, yellow_diamond, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_star, red_hexagon), (green_diamond, yellow_circle), (green_hexagon, yellow_diamond), (red_diamond, yellow_triangle)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell046_seed00046004","image":"images/path_test_cell046_seed00046004.png","image_sha256":"6efcd73bb507e329b60a3d02b365cf770e3b513956a796fe45144aeb3314fc95","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, blue_hexagon, blue_star, orange_triangle, purple_diamond, purple_hexagon, purple_star, red_diamond, red_star, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, blue_star), (blue_hexagon, purple_hexagon), (orange_triangle, purple_diamond), (purple_star, yellow_triangle), (red_diamond, red_star)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell047_seed00047000","image":"images/path_test_cell047_seed00047000.png","image_sha256":"fd2e2f7297356fd10cb074bb8ab26f3c92fcaf95e00d2010fec475aba3e47ebe","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, green_circle, green_hexagon, green_star, orange_diamond, purple_diamond, purple_hexagon, purple_square, purple_star, yellow_diamond}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, green_star), (green_circle, yellow_diamond), (green_hexagon, purple_star), (orange_diamond, purple_diamond), (purple_hexagon, purple_square)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell047_seed00047001","image":"images/path_test_cell047_seed00047001.png","image_sha256":"f7195909a9836bc3df9dde675fbb0a09ca3ed5e88212bab304110f778a16b745","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, blue_triangle, green_diamond, green_square, green_star, orange_diamond, purple_diamond, purple_triangle, yellow_square, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, yellow_triangle), (blue_triangle, purple_diamond), (green_diamond, purple_triangle), (green_square, orange_diamond), (green_star, yellow_square)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell047_seed00047002","image":"images/path_test_cell047_seed00047002.png","image_sha256":"3a88d2880d971d475b4ea2530d2fbd431ba43e22188955551db1928ddaa03a71","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_hexagon, blue_square, blue_star, green_square, orange_circle, purple_star, red_circle, yellow_hexagon}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_hexagon, green_square), (blue_square, orange_circle), (blue_star, yellow_hexagon), (purple_star, red_circle)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell047_seed00047003","image":"images/path_test_cell047_seed00047003.png","image_sha256":"6ec4324bcd7a8bd52e029ccd028dca52f3b819bf89a3041564dca548d44d3af6","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, blue_hexagon, blue_triangle, green_square, green_star, purple_triangle, red_square, yellow_hexagon, yellow_square, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, green_square), (blue_hexagon, yellow_square), (blue_triangle, red_square), (green_star, purple_triangle), (yellow_hexagon, yellow_star)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell047_seed00047004","image":"images/path_test_cell047_seed00047004.png","image_sha256":"9ad655340d046fe8a91851b28c45fc6ac542f882b16669fc8bb28668e8042ea3","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_hexagon, green_circle, green_square, orange_diamond, purple_hexagon, purple_square, red_hexagon, red_star, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, blue_hexagon), (green_circle, purple_square), (green_square, orange_diamond), (purple_hexagon, red_star), (red_hexagon, yellow_triangle)}.","difficulty":"medium","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell048_seed00048000","image":"images/path_test_cell048_seed00048000.png","image_sha256":"ba1e590bb8cc3ecc5c239e62abd6216f0bfac4067f8152e388985577365031bf","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, F, H, J, K, L, N, O, P, R, X, Y}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, N), (F, O), (H, Y), (J, K), (L, X), (P, R)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell048_seed00048001","image":"images/path_test_cell048_seed00048001.png","image_sha256":"915e0c0a0f17f73e0d4bbb3b2a5d1b49c1e287a313d592744e81ea87e70c08c5","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {D, E, F, G, L, N, O, Q, T, V, W, X, Y, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(D, W), (E, N), (F, L), (G, Y), (O, T), (Q, X), (V, Z)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell048_seed00048002","image":"images/path_test_cell048_seed00048002.png","image_sha256":"9cd4050f8b0a17215ba7996ece5792c53abe7fcbb2b4bfe3ff0f56c8a17c7ee1","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {F, G, H, I, K, M, P, Q, S, U, X, Y}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(F, X), (G, H), (I, S), (K, Q), (M, Y), (P, U)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell048_seed00048003","image":"images/path_test_cell048_seed00048003.png","image_sha256":"267886e68900774898d88dabb20c6c13583a96b68324e38f3f942422025b7075","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {C, D, F, I, K, L, O, S, T, U, W, X}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(C, I), (D, X), (F, T), (K, W), (L, O), (S, U)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell048_seed00048004","image":"images/path_test_cell048_seed00048004.png","image_sha256":"37e58f2eb1471e4849965af4824c3964363039cfb6aab1ae6af2c66a121207e7","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, C, F, H, K, M, N, R, S, U, V, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, K), (C, H), (F, M), (N, R), (S, V), (U, Z)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell049_seed00049000","image":"images/path_test_cell049_seed00049000.png","image_sha256":"f99b3bb6176abae5996c191fdd1e99ed8b9fc664ed1a36d6f4ff198c28d7abce","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {D, E, F, G, H, I, J, M, U, V, W, X, Y, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(D, I), (E, H), (F, J), (G, M), (U, W), (V, Z), (X, Y)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell049_seed00049001","image":"images/path_test_cell049_seed00049001.png","image_sha256":"9d409d4cec2039e3a039b43e74e4bb025306e0d2bfa86893bce5c7ab77a1a2d6","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, C, E, H, J, K, L, M, Q, R, S, T, V, X}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, J), (C, E), (H, K), (L, M), (Q, T), (R, V), (S, X)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell049_seed00049002","image":"images/path_test_cell049_seed00049002.png","image_sha256":"292978896a78dc3b5effea715ecd726451aace506ae859777f1145f106e4bdc3","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, C, E, I, J, K, N, O, R, T, W, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, N), (C, I), (E, R), (J, W), (K, T), (O, Z)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell049_seed00049003","image":"images/path_test_cell049_seed00049003.png","image_sha256":"31384c832b679ccfbedc2e023c809b0b2309ff3ae2c6170faa7f3ad184c6bd77","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, B, C, D, E, F, G, I, J, P, S, T, U, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, Z), (B, S), (C, J), (D, I), (E, T), (F, G), (P, U)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell049_seed00049004","image":"images/path_test_cell049_seed00049004.png","image_sha256":"6f23ce2dc66d627bc7d6d7b06cd5c06dfe381aa6c1bf41b738cef2825b70ba7d","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, B, C, E, F, H, J, K, L, O, S, V, W, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, O), (B, J), (C, Z), (E, V), (F, K), (H, L), (S, W)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell050_seed00050000","image":"images/path_test_cell050_seed00050000.png","image_sha256":"5a0c923396ac3acc24357a9db089358023aaef43173e65f4f34e2caf772920d6","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, B, C, D, E, I, J, K, M, Q, U, V}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, D), (B, C), (E, M), (I, J), (K, Q), (U, V)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell050_seed00050001","image":"images/path_test_cell050_seed00050001.png","image_sha256":"89fd84c735e06e91863e0e0214c548e0a15b13300081bfc0f7056734388b35cf","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {D, E, F, H, I, K, O, P, S, T, Y, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(D, Y), (E, O), (F, K), (H, T), (I, P), (S, Z)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell050_seed00050002","image":"images/path_test_cell050_seed00050002.png","image_sha256":"88e30caef8509e029231a8ceabf44aef354dfc2353eade30a465bc075c0883b6","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, C, D, E, G, I, L, N, O, R, T, W, Y, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, O), (C, T), (D, I), (E, W), (G, R), (L, N), (Y, Z)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell050_seed00050003","image":"images/path_test_cell050_seed00050003.png","image_sha256":"5312dbf84144888494098e075b885c6a7b57ad10b57ecc8cb78823f02bc39119","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, C, D, G, H, J, O, P, Q, R, T, U}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, J), (C, P), (D, U), (G, H), (O, Q), (R, T)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell050_seed00050004","image":"images/path_test_cell050_seed00050004.png","image_sha256":"89375918d00730da30b7896d3aace4ecacd5a4fc723a09f90f022204a7f36a00","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, C, D, E, J, M, O, P, Q, R, V, Y}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, Y), (C, O), (D, J), (E, V), (M, R), (P, Q)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell051_seed00051000","image":"images/path_test_cell051_seed00051000.png","image_sha256":"79284e002f06eaf943bb02b69c55a7b51ae901db6cc472bf57e94c0badeaeafe","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, E, F, H, I, J, P, Q, R, S, T, U, X, Y}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, Y), (E, R), (F, J), (H, S), (I, X), (P, T), (Q, U)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell051_seed00051001","image":"images/path_test_cell051_seed00051001.png","image_sha256":"22ff558f29d9a294fe38f3b65e006a0b3ce9d134fb7ef5f3771a84cfbcee2057","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {C, G, H, M, N, P, Q, U, V, W, X, Y}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(C, W), (G, U), (H, P), (M, N), (Q, Y), (V, X)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell051_seed00051002","image":"images/path_test_cell051_seed00051002.png","image_sha256":"bd95395d90a94845717d5dc6e13d1f9c323bce5584e3d7f5debb483e221392c4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, C, D, E, G, K, M, O, S, T, U, V}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, U), (C, K), (D, T), (E, S), (G, M), (O, V)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell051_seed00051003","image":"images/path_test_cell051_seed00051003.png","image_sha256":"ffe097229c1fdc2e13f3cb1967b5a52633f0bfe059d9b228234944f2e3688863","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, C, D, E, F, H, K, L, N, O, P, Q, R, V}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, R), (C, P), (D, N), (E, H), (F, K), (L, Q), (O, V)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell051_seed00051004","image":"images/path_test_cell051_seed00051004.png","image_sha256":"a5b4792fd0cd372dd581f13b606a2e44bfc8f6c4770b5a9ca2ea5094be0634ef","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, D, E, F, G, H, I, L, O, Q, R, U, X, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, H), (D, I), (E, Q), (F, U), (G, O), (L, R), (X, Z)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell052_seed00052000","image":"images/path_test_cell052_seed00052000.png","image_sha256":"b27238f90d16153970b08851cb01c35c6b4fe6cd39785f44f2e17cfbafe6a446","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, B, C, H, I, K, L, M, O, P, R, U, V, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, I), (B, M), (C, V), (H, P), (K, O), (L, U), (R, Z)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell052_seed00052001","image":"images/path_test_cell052_seed00052001.png","image_sha256":"58d408f38ebc25c354f37c5942de9deec03e1d5df57331c3f90569571dc2e296","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, C, H, I, K, L, P, R, S, W, X, Y}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, X), (C, L), (H, I), (K, R), (P, S), (W, Y)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell052_seed00052002","image":"images/path_test_cell052_seed00052002.png","image_sha256":"cf3b65c44ffd2c8f9460baea1306ebd447cfa76527475dcfb9e570467aa5bcf5","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, E, F, H, J, M, N, O, P, Q, R, S}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, H), (E, Q), (F, N), (J, R), (M, O), (P, S)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell052_seed00052003","image":"images/path_test_cell052_seed00052003.png","image_sha256":"d8a602dab72449079cea5d638753218c75de947c02b35c4369ce43cfd15b3f19","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, B, E, I, K, L, M, Q, T, U, V, X}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, X), (B, E), (I, L), (K, V), (M, T), (Q, U)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell052_seed00052004","image":"images/path_test_cell052_seed00052004.png","image_sha256":"c2aa4660e9f9e1658b170d6827ead229439df353fb2eaa8fe3c7b604b8d4ed1b","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, C, D, E, G, L, M, N, P, Q, T, U, V, W}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, T), (C, P), (D, N), (E, U), (G, L), (M, W), (Q, V)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell053_seed00053000","image":"images/path_test_cell053_seed00053000.png","image_sha256":"635e37bba67c475ce17bb2156abe806dee3d15fa5b66146a1c2c21052563922a","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, F, G, H, J, K, L, Q, S, T, U, X}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, Q), (F, J), (G, S), (H, X), (K, L), (T, U)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell053_seed00053001","image":"images/path_test_cell053_seed00053001.png","image_sha256":"e1dcd38f9afc98a1aa9eab2b6992debe63704f0abe2db831461a14b99a4f433c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, B, F, I, J, L, O, Q, T, U, X, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, O), (B, Q), (F, T), (I, Z), (J, L), (U, X)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell053_seed00053002","image":"images/path_test_cell053_seed00053002.png","image_sha256":"7415a1a9438f531c89859afabaff2d610e1349cb003f686a69afb2360fa38804","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, B, F, G, H, I, J, K, Q, R, S, T, U, V}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, R), (B, J), (F, T), (G, H), (I, S), (K, U), (Q, V)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell053_seed00053003","image":"images/path_test_cell053_seed00053003.png","image_sha256":"bc3db054e9ab280085e2d8df61f14845cec2a6e222c0dedfa330294f6eb7c9af","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {B, C, E, I, J, L, N, Q, R, S, T, V, X, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(B, L), (C, V), (E, R), (I, Q), (J, Z), (N, X), (S, T)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell053_seed00053004","image":"images/path_test_cell053_seed00053004.png","image_sha256":"d493b1e0879c7e9290e2744c97574d1fc37bfcf671fc6a4623935c56d2783782","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {A, H, I, K, L, M, Q, R, U, W, Y, Z}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(A, W), (H, M), (I, L), (K, U), (Q, Z), (R, Y)}.","difficulty":"hard","endpoint_type":"letter"} | |
| {"sample_id":"path_test_cell054_seed00054000","image":"images/path_test_cell054_seed00054000.png","image_sha256":"10f80f8f8234086953d1723d76b64af75b6d6df2fbeaee9c2bd8758339d92f44","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {11, 22, 29, 32, 33, 34, 40, 47, 52, 58, 64, 78, 79, 99}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(11, 64), (22, 34), (29, 58), (32, 99), (33, 78), (40, 79), (47, 52)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell054_seed00054001","image":"images/path_test_cell054_seed00054001.png","image_sha256":"2373376336c480c9677eddb75304a094ec6eaf3abd9f874771a90aeca7d37b2c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {3, 8, 30, 32, 38, 50, 54, 71, 79, 80, 87, 91}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(3, 38), (8, 91), (30, 71), (32, 79), (50, 80), (54, 87)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell054_seed00054002","image":"images/path_test_cell054_seed00054002.png","image_sha256":"689cd228812f3537886f9fc61ad2f7e398c742a9debaa8e40c3b2f6f85cbc4d3","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {22, 31, 33, 40, 45, 47, 56, 64, 68, 70, 79, 91, 92, 95}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(22, 79), (31, 47), (33, 70), (40, 91), (45, 68), (56, 92), (64, 95)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell054_seed00054003","image":"images/path_test_cell054_seed00054003.png","image_sha256":"4def6a4217b644ea615741946fc3768eefd7ba38c82996b80776e91e296fc6a4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {17, 22, 34, 36, 37, 48, 66, 68, 71, 72, 84, 85}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(17, 71), (22, 68), (34, 85), (36, 48), (37, 84), (66, 72)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell054_seed00054004","image":"images/path_test_cell054_seed00054004.png","image_sha256":"b1f40e79d7e8e4dd4756a32da17d390e311e0f95f3ae44acd687f887b6eb78ff","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {2, 8, 26, 42, 49, 56, 64, 66, 86, 91, 92, 99}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(2, 64), (8, 56), (26, 91), (42, 66), (49, 92), (86, 99)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell055_seed00055000","image":"images/path_test_cell055_seed00055000.png","image_sha256":"012116524116f918d701e11c7431f7e6593cbb3b5d269790eda1b22294a9d091","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {12, 13, 25, 31, 35, 42, 43, 47, 72, 78, 87, 89, 92, 98}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(12, 47), (13, 98), (25, 42), (31, 92), (35, 72), (43, 78), (87, 89)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell055_seed00055001","image":"images/path_test_cell055_seed00055001.png","image_sha256":"82e1fdc5743094ac6f1da8e8339e74773363930fd92415f13fe731c70331b579","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {3, 5, 6, 12, 41, 43, 44, 57, 64, 70, 83, 85}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(3, 12), (5, 44), (6, 64), (41, 83), (43, 85), (57, 70)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell055_seed00055002","image":"images/path_test_cell055_seed00055002.png","image_sha256":"73bf2a6c7f8c5d1442698190048e028a87a8b2b3a1dfd1fe45f057a794b72b1b","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {6, 8, 12, 15, 21, 33, 46, 59, 72, 73, 78, 87}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(6, 59), (8, 15), (12, 78), (21, 33), (46, 87), (72, 73)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell055_seed00055003","image":"images/path_test_cell055_seed00055003.png","image_sha256":"ba69cbb47256a3963adab19bdec39df402197051f16c57e6f6e7931d4ade77d9","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {5, 8, 11, 29, 38, 40, 43, 45, 55, 60, 68, 71, 73, 91}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(5, 38), (8, 71), (11, 60), (29, 43), (40, 68), (45, 73), (55, 91)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell055_seed00055004","image":"images/path_test_cell055_seed00055004.png","image_sha256":"7be48e53a775fb82f1bfc48d2b1f1c59273d358fbf83d89350696a319f02f193","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {11, 35, 37, 40, 41, 43, 48, 58, 64, 69, 70, 79, 94, 98}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(11, 79), (35, 41), (37, 98), (40, 69), (43, 64), (48, 94), (58, 70)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell056_seed00056000","image":"images/path_test_cell056_seed00056000.png","image_sha256":"f4a199d4b9a454cd42cb26d88faa4d8bb9cc0445ff10c85948b3776d97fa3acd","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {1, 7, 12, 27, 28, 42, 49, 51, 65, 72, 79, 82, 94, 97}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(1, 49), (7, 82), (12, 72), (27, 51), (28, 65), (42, 97), (79, 94)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell056_seed00056001","image":"images/path_test_cell056_seed00056001.png","image_sha256":"cd9ca7120c4d4f056002160b8765ede2612f8a5d56bef6bf9ece8471b4bdb926","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {17, 38, 39, 43, 44, 47, 54, 61, 63, 71, 86, 95}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(17, 61), (38, 86), (39, 71), (43, 44), (47, 63), (54, 95)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell056_seed00056002","image":"images/path_test_cell056_seed00056002.png","image_sha256":"8f3258979537d8538e1a11fe7e98fd532840cc2d4e87b32d835fbad0fcf97551","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {3, 5, 11, 12, 30, 39, 54, 62, 63, 69, 78, 97}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(3, 30), (5, 97), (11, 12), (39, 63), (54, 62), (69, 78)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell056_seed00056003","image":"images/path_test_cell056_seed00056003.png","image_sha256":"b78e56b3a0dd1a414c7a48ea9e6799cf92233cb4175d2ab2ca7c6713881ea172","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {12, 18, 47, 49, 51, 59, 62, 63, 64, 68, 71, 78, 87, 97}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(12, 64), (18, 97), (47, 49), (51, 59), (62, 71), (63, 87), (68, 78)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell056_seed00056004","image":"images/path_test_cell056_seed00056004.png","image_sha256":"b23ab0681b816eac873571d665f1ad659dbf1d12337c3e1dc6150ff93d50da19","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {3, 17, 19, 60, 66, 67, 69, 75, 76, 77, 82, 84}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(3, 69), (17, 19), (60, 75), (66, 67), (76, 84), (77, 82)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell057_seed00057000","image":"images/path_test_cell057_seed00057000.png","image_sha256":"ad15b48b76feb29da7110cfa282e1f32d27baf65c6f9e68c945c10df14284502","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {9, 13, 14, 15, 29, 33, 47, 50, 59, 61, 73, 74}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(9, 14), (13, 15), (29, 61), (33, 73), (47, 50), (59, 74)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell057_seed00057001","image":"images/path_test_cell057_seed00057001.png","image_sha256":"1b558c2edc906924cc6e2c96a9d333f985ad51318143eb87cc3ff4d5defe55c0","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {4, 12, 43, 50, 51, 73, 79, 81, 91, 94, 95, 97}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(4, 95), (12, 73), (43, 94), (50, 97), (51, 81), (79, 91)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell057_seed00057002","image":"images/path_test_cell057_seed00057002.png","image_sha256":"736bc94653c6c2e719604b0aecb856ee087b389bf8f4a5c9afc3ba071d940dcd","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {1, 16, 27, 45, 47, 48, 62, 68, 77, 90, 94, 97}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(1, 68), (16, 90), (27, 47), (45, 48), (62, 97), (77, 94)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell057_seed00057003","image":"images/path_test_cell057_seed00057003.png","image_sha256":"a19ca6bf4eeb9232aef2e6d779540562dce27e4968ed9a448393c798dcc5ab01","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {6, 21, 23, 35, 42, 45, 49, 57, 65, 69, 78, 94}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(6, 49), (21, 35), (23, 65), (42, 78), (45, 57), (69, 94)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell057_seed00057004","image":"images/path_test_cell057_seed00057004.png","image_sha256":"a50d65d8a2ce76ce6680427548bd7015ceb4f1d649be97c5d31a258fd79b0631","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {6, 7, 16, 28, 35, 44, 47, 55, 66, 70, 80, 91, 97, 99}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(6, 35), (7, 66), (16, 91), (28, 47), (44, 70), (55, 99), (80, 97)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell058_seed00058000","image":"images/path_test_cell058_seed00058000.png","image_sha256":"10ec93fdc9693c25ab17fe186e1da4cca44af38261e792f651f994ea81e55ea1","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {5, 17, 25, 43, 44, 45, 57, 65, 67, 70, 79, 81, 92, 99}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(5, 45), (17, 99), (25, 79), (43, 44), (57, 67), (65, 70), (81, 92)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell058_seed00058001","image":"images/path_test_cell058_seed00058001.png","image_sha256":"77b9c16e0971d1fc94e26a18a6f7b20578d4385603f228f016612a95e91ec657","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {1, 3, 5, 6, 10, 15, 21, 23, 24, 75, 77, 80, 86, 94}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(1, 86), (3, 24), (5, 23), (6, 15), (10, 75), (21, 94), (77, 80)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell058_seed00058002","image":"images/path_test_cell058_seed00058002.png","image_sha256":"dec0acef0d0699173202933cf0600152c18bb596d4e506822e705d8b4f3b5cab","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {7, 16, 18, 22, 25, 36, 51, 56, 61, 71, 78, 88}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(7, 71), (16, 36), (18, 88), (22, 78), (25, 51), (56, 61)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell058_seed00058003","image":"images/path_test_cell058_seed00058003.png","image_sha256":"ae94a90b6a1bd6ba6397fefddeeede0b97b7ecc9375f14b81e484d8289d68ce9","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {13, 14, 19, 21, 30, 34, 35, 45, 51, 64, 67, 75, 79, 81}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(13, 21), (14, 35), (19, 81), (30, 79), (34, 51), (45, 64), (67, 75)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell058_seed00058004","image":"images/path_test_cell058_seed00058004.png","image_sha256":"a29dbbed977bf6cb28cd8ec0020f24853a4fcfcc3957eb1a264f54cc9d8d8323","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {5, 22, 25, 34, 35, 37, 38, 65, 66, 67, 68, 83}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(5, 34), (22, 67), (25, 68), (35, 37), (38, 83), (65, 66)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell059_seed00059000","image":"images/path_test_cell059_seed00059000.png","image_sha256":"51549c37476eb5c1c6b69f9adf588165f195e28a7af8664ae7124b16f11269e9","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {1, 7, 9, 15, 19, 27, 29, 32, 43, 46, 51, 68, 79, 84}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(1, 79), (7, 9), (15, 29), (19, 43), (27, 46), (32, 68), (51, 84)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell059_seed00059001","image":"images/path_test_cell059_seed00059001.png","image_sha256":"defced78864084468c5f77f7443243b6d71f167dcbeeba4689f96a93ca9039d5","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {16, 17, 18, 31, 43, 45, 46, 56, 62, 71, 79, 83}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(16, 45), (17, 79), (18, 31), (43, 83), (46, 56), (62, 71)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell059_seed00059002","image":"images/path_test_cell059_seed00059002.png","image_sha256":"fe0c1bf636f340ce22dea7efc31c9423e833c2d5abb330c78bcbf0d7a9a8b431","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {8, 9, 16, 26, 30, 39, 44, 55, 57, 82, 92, 95}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(8, 16), (9, 44), (26, 57), (30, 55), (39, 95), (82, 92)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell059_seed00059003","image":"images/path_test_cell059_seed00059003.png","image_sha256":"075df5f13aa05d0205b73f5da0dc6019f3e2c5f44f4d365bac5f4daf5d37e02a","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {6, 9, 10, 11, 30, 37, 39, 58, 67, 80, 92, 99}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(6, 30), (9, 92), (10, 99), (11, 67), (37, 80), (39, 58)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell059_seed00059004","image":"images/path_test_cell059_seed00059004.png","image_sha256":"a7552fc0ccdc45f2562611186d07576efda84f416ba8fd1cf13f5db1646099f7","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {11, 15, 18, 19, 22, 23, 29, 30, 35, 46, 74, 78, 80, 84}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(11, 23), (15, 18), (19, 78), (22, 30), (29, 35), (46, 74), (80, 84)}.","difficulty":"hard","endpoint_type":"number"} | |
| {"sample_id":"path_test_cell060_seed00060000","image":"images/path_test_cell060_seed00060000.png","image_sha256":"a6c781dbdaa69189d62ad0e9404f31ad6b9bd695ca0b7cc24d99ec18ca49e13a","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, cat, crown, diamond_shape, dog, frog, hammer, heart, light_bulb, mushroom, star, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, star), (cat, diamond_shape), (crown, heart), (dog, light_bulb), (frog, mushroom), (hammer, sun)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell060_seed00060001","image":"images/path_test_cell060_seed00060001.png","image_sha256":"14c68ab8bb289c162e4a050ad8e0c38d38584fa4ecc2af1819cc5f181d4d8d2c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {banana, cake, crown, diamond_shape, dog, heart, light_bulb, lock, octopus, rocket, scissors, star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(banana, diamond_shape), (cake, star), (crown, octopus), (dog, light_bulb), (heart, scissors), (lock, rocket)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell060_seed00060002","image":"images/path_test_cell060_seed00060002.png","image_sha256":"95c315ab408c07a7888b57fba606b03558145cc508d9ca972907a2a88c564c6e","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {apple, banana, carrot, cat, crown, dog, key, light_bulb, moon, owl, pizza, rocket, snake, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(apple, pizza), (banana, cat), (carrot, sun), (crown, snake), (dog, light_bulb), (key, owl), (moon, rocket)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell060_seed00060003","image":"images/path_test_cell060_seed00060003.png","image_sha256":"5f2ea0bcc740fd2fbd800c713924093203812d424339dc6804536483e5e8c9ab","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {banana, bee, butterfly, cake, cloud, dog, fish, gift, light_bulb, lightning, music_note, owl, rocket, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(banana, butterfly), (bee, fish), (cake, owl), (cloud, sun), (dog, rocket), (gift, music_note), (light_bulb, lightning)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell060_seed00060004","image":"images/path_test_cell060_seed00060004.png","image_sha256":"09e8a5ee33ec2e67d51f1006f25c5df014a273a1782e78f3741afa02b67f3ff0","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, balloon, bee, cake, carrot, frog, key, lightning, lock, owl, snowflake, star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, frog), (balloon, carrot), (bee, lightning), (cake, key), (lock, owl), (snowflake, star)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell061_seed00061000","image":"images/path_test_cell061_seed00061000.png","image_sha256":"ee45c748c2156c5b7dab8fc4397ee40ba1b96c021c74a7bbe83fe7fee975c313","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {banana, cat, crown, flower, frog, hammer, heart, lock, mushroom, owl, scissors, snake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(banana, scissors), (cat, mushroom), (crown, frog), (flower, snake), (hammer, heart), (lock, owl)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell061_seed00061001","image":"images/path_test_cell061_seed00061001.png","image_sha256":"558357158699161ebe4c7e637bee1ecd20e22501a0804d546b7c97c298d05e0e","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, apple, bee, cookie, flower, gift, hammer, heart, lightning, lock, mushroom, octopus, scissors, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, sun), (apple, mushroom), (bee, lightning), (cookie, scissors), (flower, lock), (gift, hammer), (heart, octopus)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell061_seed00061002","image":"images/path_test_cell061_seed00061002.png","image_sha256":"492d0d9f4eda0990e56fd9b9804f037d6cae7d9624d5cb7dec0b3065e2d6e6cc","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {apple, balloon, dog, gift, hammer, key, lock, magnet, mushroom, music_note, snowflake, star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(apple, magnet), (balloon, star), (dog, hammer), (gift, lock), (key, snowflake), (mushroom, music_note)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell061_seed00061003","image":"images/path_test_cell061_seed00061003.png","image_sha256":"24f2e917b6514847bce038b8a09b546746c560eae3fed33c8797acc1a660c583","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, banana, carrot, cat, cloud, cookie, dog, flower, heart, lightning, lock, magnet, pizza, snake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, cloud), (banana, cookie), (carrot, lightning), (cat, dog), (flower, lock), (heart, snake), (magnet, pizza)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell061_seed00061004","image":"images/path_test_cell061_seed00061004.png","image_sha256":"3c77a06e0a47ffd351f5be25fd28760bc689eabdcd91966b1d8e3232d9442571","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {cloud, fish, gift, heart, key, lightning, magnet, moon, mushroom, music_note, scissors, snake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(cloud, gift), (fish, heart), (key, magnet), (lightning, scissors), (moon, snake), (mushroom, music_note)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell062_seed00062000","image":"images/path_test_cell062_seed00062000.png","image_sha256":"3a59a8c593508687da431e3902a6c38354a2dc2bae8be1ca4bafea56aaac8361","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {banana, carrot, cat, crown, dog, fish, hammer, heart, magnet, mushroom, rocket, snake, snowflake, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(banana, dog), (carrot, hammer), (cat, snake), (crown, magnet), (fish, heart), (mushroom, sun), (rocket, snowflake)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell062_seed00062001","image":"images/path_test_cell062_seed00062001.png","image_sha256":"bb5532c52f0bd8168de1740141cf324149d3d420f7e19acb48215a054526df79","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {banana, blue_circle, carrot, crown, diamond_shape, fire, fish, flower, hammer, light_bulb, moon, mushroom, scissors, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(banana, diamond_shape), (blue_circle, fish), (carrot, flower), (crown, moon), (fire, sun), (hammer, light_bulb), (mushroom, scissors)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell062_seed00062002","image":"images/path_test_cell062_seed00062002.png","image_sha256":"206badaeabe8a4e461ed377c9b4af86b51a7f4ac8b5b9eda119846012f8c4a6d","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, balloon, crown, dog, fire, hammer, key, light_bulb, lightning, lock, owl, pizza, snake, star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, pizza), (balloon, light_bulb), (crown, snake), (dog, key), (fire, lock), (hammer, lightning), (owl, star)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell062_seed00062003","image":"images/path_test_cell062_seed00062003.png","image_sha256":"6403e3fc3a9c381fab064d9e05d5adb88c33fb67991cab297903bca4d541e5ed","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {balloon, banana, bee, butterfly, carrot, cloud, cookie, diamond_shape, fire, flower, hammer, lightning, octopus, rocket}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(balloon, lightning), (banana, cloud), (bee, rocket), (butterfly, carrot), (cookie, hammer), (diamond_shape, octopus), (fire, flower)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell062_seed00062004","image":"images/path_test_cell062_seed00062004.png","image_sha256":"418a49aca5377786c10b47b8d9f259f5e0636ace05cca542d354dca1f3933b40","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {bee, blue_circle, butterfly, cake, cat, fire, flower, frog, heart, key, lock, magnet, rocket, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(bee, key), (blue_circle, cat), (butterfly, heart), (cake, frog), (fire, flower), (lock, magnet), (rocket, sun)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell063_seed00063000","image":"images/path_test_cell063_seed00063000.png","image_sha256":"76399a33cdc2cf04e2e1798a135ea2f9a4ff4147e5b5aefff2a5b6ce609fbc76","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, balloon, banana, bee, carrot, cookie, crown, fire, hammer, heart, magnet, moon, owl, star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, magnet), (balloon, heart), (banana, cookie), (bee, hammer), (carrot, fire), (crown, moon), (owl, star)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell063_seed00063001","image":"images/path_test_cell063_seed00063001.png","image_sha256":"a84e3e92c9d9c56952a38d760eca12f420a891dea02cbcc047d0a6b993a2458e","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {apple, cookie, diamond_shape, frog, light_bulb, lightning, lock, magnet, moon, octopus, owl, scissors}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(apple, owl), (cookie, octopus), (diamond_shape, scissors), (frog, moon), (light_bulb, lock), (lightning, magnet)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell063_seed00063002","image":"images/path_test_cell063_seed00063002.png","image_sha256":"56a67690b4a94aebdf084e038ca62ab5662c97ecb3db5e6c21a2dd80453d9689","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, balloon, bee, blue_circle, cat, cloud, fish, gift, hammer, moon, mushroom, pizza}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, gift), (balloon, bee), (blue_circle, hammer), (cat, pizza), (cloud, fish), (moon, mushroom)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell063_seed00063003","image":"images/path_test_cell063_seed00063003.png","image_sha256":"93914bf0bdb107fbaaf54e4a14a2cd8bb929061c7582dede79b7d0b44b2a79e6","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, cake, diamond_shape, fire, flower, key, moon, mushroom, octopus, owl, rocket, snake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, octopus), (cake, mushroom), (diamond_shape, fire), (flower, owl), (key, moon), (rocket, snake)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell063_seed00063004","image":"images/path_test_cell063_seed00063004.png","image_sha256":"01c768136641484b7b94619dd1b121b4822aefb295488e235112d159bbf176c3","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, bee, blue_circle, butterfly, cat, cloud, cookie, frog, hammer, key, light_bulb, lightning, mushroom, rocket}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, key), (bee, frog), (blue_circle, butterfly), (cat, cookie), (cloud, light_bulb), (hammer, lightning), (mushroom, rocket)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell064_seed00064000","image":"images/path_test_cell064_seed00064000.png","image_sha256":"efaccce8228e6fb9fb742feaefb2a928e30db606c541b7c4f96ebf09f6d7e902","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, apple, butterfly, carrot, cat, flower, hammer, key, light_bulb, lock, music_note, snowflake, star, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, carrot), (apple, lock), (butterfly, sun), (cat, star), (flower, hammer), (key, light_bulb), (music_note, snowflake)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell064_seed00064001","image":"images/path_test_cell064_seed00064001.png","image_sha256":"a2ee824c295b07e31c6054d04048ece4b93129204eaedab6e4d794d82d196fa4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, apple, cat, fish, heart, key, magnet, mushroom, octopus, owl, pizza, rocket, snowflake, star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, heart), (apple, mushroom), (cat, snowflake), (fish, key), (magnet, star), (octopus, rocket), (owl, pizza)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell064_seed00064002","image":"images/path_test_cell064_seed00064002.png","image_sha256":"a830ff7b03d6290b6dac8b269f55f4f9877616a749ac29704750f204711ef2db","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, blue_circle, cat, cloud, dog, fire, frog, gift, key, light_bulb, lightning, moon, music_note, rocket}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, lightning), (blue_circle, frog), (cat, dog), (cloud, gift), (fire, rocket), (key, moon), (light_bulb, music_note)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell064_seed00064003","image":"images/path_test_cell064_seed00064003.png","image_sha256":"407a83cd1798955ff88822ebc0a875869a678ec7c102a48cac936920c89f2d3c","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, balloon, cake, carrot, cat, crown, frog, hammer, magnet, octopus, pizza, snake, snowflake, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, crown), (balloon, frog), (cake, hammer), (carrot, pizza), (cat, snowflake), (magnet, snake), (octopus, sun)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell064_seed00064004","image":"images/path_test_cell064_seed00064004.png","image_sha256":"ac29c114b360b1d8b145fbbbeea04c4c6f644ca0e1d4ef2095a49aad252ffba8","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {anchor, butterfly, cake, carrot, cloud, cookie, crown, heart, lightning, lock, mushroom, scissors, star, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(anchor, mushroom), (butterfly, cloud), (cake, lightning), (carrot, cookie), (crown, scissors), (heart, lock), (star, sun)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell065_seed00065000","image":"images/path_test_cell065_seed00065000.png","image_sha256":"3efe7e97d4af38f2af65ec53d471f2230f50392821c408ac4428b3e437223c77","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {balloon, banana, bee, cake, cloud, cookie, diamond_shape, flower, lightning, music_note, scissors, star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(balloon, bee), (banana, scissors), (cake, flower), (cloud, diamond_shape), (cookie, star), (lightning, music_note)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell065_seed00065001","image":"images/path_test_cell065_seed00065001.png","image_sha256":"b13b58359b7529407c32d4955326c9cd61a331da82db6394c67690b5038dcfd9","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {apple, balloon, banana, carrot, crown, fish, flower, key, moon, octopus, pizza, rocket, star, sun}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(apple, key), (balloon, carrot), (banana, crown), (fish, sun), (flower, moon), (octopus, pizza), (rocket, star)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell065_seed00065002","image":"images/path_test_cell065_seed00065002.png","image_sha256":"af922fef386b005b1dde9b54ca3b2933081413fc1dd8dd580a1adc4a9a066fdf","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {butterfly, cookie, diamond_shape, fire, flower, gift, heart, key, light_bulb, moon, owl, pizza, snowflake, star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(butterfly, moon), (cookie, diamond_shape), (fire, gift), (flower, snowflake), (heart, star), (key, pizza), (light_bulb, owl)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell065_seed00065003","image":"images/path_test_cell065_seed00065003.png","image_sha256":"0947f850dc59823f32f83f8a9754bb3194139f35b59d4c4cc7db282caeda674d","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {butterfly, cake, fire, flower, frog, hammer, heart, lightning, lock, magnet, mushroom, music_note, owl, snake}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(butterfly, hammer), (cake, music_note), (fire, lightning), (flower, mushroom), (frog, lock), (heart, owl), (magnet, snake)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell065_seed00065004","image":"images/path_test_cell065_seed00065004.png","image_sha256":"613f7d063fc41fde7c8bf35ab10ca29e339caebc5579f45c079afa0444b2027f","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {balloon, dog, gift, lightning, lock, moon, music_note, pizza, rocket, snake, snowflake, star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(balloon, star), (dog, lock), (gift, snowflake), (lightning, music_note), (moon, rocket), (pizza, snake)}.","difficulty":"hard","endpoint_type":"icon"} | |
| {"sample_id":"path_test_cell066_seed00066000","image":"images/path_test_cell066_seed00066000.png","image_sha256":"38b205662593f2b5b2dc60836aecd68caf048b66e0b98d30d608e9774349b2b1","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_square, blue_star, green_triangle, orange_diamond, purple_circle, purple_diamond, purple_hexagon, purple_star, red_square, red_triangle, yellow_circle, yellow_diamond, yellow_star, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_square, red_square), (blue_star, purple_star), (green_triangle, red_triangle), (orange_diamond, purple_hexagon), (purple_circle, yellow_circle), (purple_diamond, yellow_diamond), (yellow_star, yellow_triangle)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell066_seed00066001","image":"images/path_test_cell066_seed00066001.png","image_sha256":"a04ab2ceeebe8238509bc5135a354ccba25b15c3bec3a4d30c58a68582418141","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, green_circle, green_diamond, green_hexagon, green_square, green_star, orange_star, orange_triangle, purple_square, purple_star, purple_triangle, yellow_diamond, yellow_square, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, purple_star), (green_circle, yellow_diamond), (green_diamond, yellow_square), (green_hexagon, yellow_triangle), (green_square, green_star), (orange_star, orange_triangle), (purple_square, purple_triangle)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell066_seed00066002","image":"images/path_test_cell066_seed00066002.png","image_sha256":"41e16db85e40861304198da2e28e6e913779b0853cdab81f3ec9a9e971511efb","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_diamond, blue_square, green_circle, orange_diamond, orange_square, orange_triangle, purple_diamond, purple_square, red_diamond, red_triangle, yellow_circle, yellow_diamond, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, orange_triangle), (blue_diamond, yellow_diamond), (blue_square, orange_diamond), (green_circle, yellow_circle), (orange_square, red_diamond), (purple_diamond, yellow_star), (purple_square, red_triangle)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell066_seed00066003","image":"images/path_test_cell066_seed00066003.png","image_sha256":"0bddfc6496a3b8f4eb320944c0662e32d38519f0f6b85a033f3bf883c932a05e","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, blue_star, green_circle, green_star, green_triangle, orange_triangle, purple_square, red_diamond, red_triangle, yellow_diamond, yellow_hexagon, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, orange_triangle), (blue_star, red_triangle), (green_circle, yellow_triangle), (green_star, yellow_diamond), (green_triangle, red_diamond), (purple_square, yellow_hexagon)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell066_seed00066004","image":"images/path_test_cell066_seed00066004.png","image_sha256":"d3d0dad2c88d2b00018a27bffac0a9c7e73e4eb7af8bf328b07f61451f857b20","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_hexagon, blue_square, blue_triangle, green_circle, green_hexagon, orange_diamond, orange_triangle, purple_circle, purple_hexagon, red_circle, yellow_diamond}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, green_hexagon), (blue_hexagon, blue_square), (blue_triangle, purple_circle), (green_circle, orange_diamond), (orange_triangle, yellow_diamond), (purple_hexagon, red_circle)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell067_seed00067000","image":"images/path_test_cell067_seed00067000.png","image_sha256":"950c4de13ffe08f8383c67c0da2c4d25a7023118bbec37ea00ac5189b4ceac45","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_diamond, blue_hexagon, green_circle, orange_hexagon, orange_square, orange_star, purple_hexagon, purple_triangle, red_circle, red_triangle, yellow_diamond, yellow_hexagon, yellow_square}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, red_circle), (blue_diamond, yellow_diamond), (blue_hexagon, purple_triangle), (green_circle, purple_hexagon), (orange_hexagon, orange_square), (orange_star, red_triangle), (yellow_hexagon, yellow_square)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell067_seed00067001","image":"images/path_test_cell067_seed00067001.png","image_sha256":"4c1d9023d74736a915bfce3663820c15af464379b1761a8ea51357f98b7fdadd","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, blue_hexagon, blue_triangle, green_diamond, green_triangle, orange_circle, purple_diamond, purple_triangle, red_diamond, red_star, yellow_diamond, yellow_hexagon}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, purple_diamond), (blue_hexagon, yellow_hexagon), (blue_triangle, green_diamond), (green_triangle, red_diamond), (orange_circle, yellow_diamond), (purple_triangle, red_star)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell067_seed00067002","image":"images/path_test_cell067_seed00067002.png","image_sha256":"d9493c334fdd7d76eb27cbc4bdffc933b4249c818fff51eb1393605adbc7cb55","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, blue_triangle, green_hexagon, orange_circle, orange_hexagon, orange_triangle, purple_circle, purple_triangle, red_circle, red_hexagon, red_square, red_star, yellow_circle, yellow_hexagon}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, orange_triangle), (blue_triangle, red_square), (green_hexagon, red_star), (orange_circle, yellow_hexagon), (orange_hexagon, red_circle), (purple_circle, yellow_circle), (purple_triangle, red_hexagon)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell067_seed00067003","image":"images/path_test_cell067_seed00067003.png","image_sha256":"3f689c1692846c8ffb098920f23c0260b4af1e33cf5228e0c87f70634ae005fe","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_hexagon, green_circle, orange_circle, orange_diamond, purple_diamond, purple_hexagon, purple_triangle, red_diamond, red_square, red_star, red_triangle, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_hexagon, red_triangle), (green_circle, red_diamond), (orange_circle, red_square), (orange_diamond, yellow_triangle), (purple_diamond, red_star), (purple_hexagon, purple_triangle)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell067_seed00067004","image":"images/path_test_cell067_seed00067004.png","image_sha256":"36f24c3ba18f4fbb969a9da16421a3dbff171487267307a9f82d18084bc9a479","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, blue_triangle, green_square, green_triangle, orange_diamond, orange_square, orange_star, orange_triangle, purple_diamond, purple_hexagon, yellow_square, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, orange_triangle), (blue_triangle, yellow_square), (green_square, orange_star), (green_triangle, orange_diamond), (orange_square, purple_diamond), (purple_hexagon, yellow_triangle)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell068_seed00068000","image":"images/path_test_cell068_seed00068000.png","image_sha256":"767edf9842dc32d00597f134c154b4618a6ab618d1fbd68bec20bbd6953377ed","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_hexagon, blue_triangle, orange_circle, orange_hexagon, purple_circle, purple_star, purple_triangle, red_diamond, yellow_diamond, yellow_square, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, yellow_diamond), (blue_hexagon, purple_triangle), (blue_triangle, orange_circle), (orange_hexagon, purple_star), (purple_circle, yellow_triangle), (red_diamond, yellow_square)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell068_seed00068001","image":"images/path_test_cell068_seed00068001.png","image_sha256":"58e078412a92ff1e5d159e101d8fec8d256f4548c602b7b697766e571609f6e7","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_diamond, blue_hexagon, orange_circle, orange_diamond, orange_square, purple_circle, purple_diamond, purple_star, red_circle, red_star, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, red_circle), (blue_diamond, orange_square), (blue_hexagon, purple_diamond), (orange_circle, purple_circle), (orange_diamond, purple_star), (red_star, yellow_triangle)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell068_seed00068002","image":"images/path_test_cell068_seed00068002.png","image_sha256":"70087da1c482990a4d9493ef2cb0144e5022dc31da43a90ba9cba1a794f5fd27","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, blue_hexagon, blue_star, green_circle, green_square, green_triangle, orange_circle, orange_hexagon, orange_square, orange_triangle, purple_circle, purple_diamond, red_triangle, yellow_diamond}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, blue_hexagon), (blue_star, red_triangle), (green_circle, orange_triangle), (green_square, yellow_diamond), (green_triangle, orange_square), (orange_circle, orange_hexagon), (purple_circle, purple_diamond)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell068_seed00068003","image":"images/path_test_cell068_seed00068003.png","image_sha256":"194823e15ff1a7b23fb7146da7621e5463b703b3fbd7aeddaed6ec1fc28d9972","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, green_diamond, green_hexagon, green_square, green_star, green_triangle, orange_circle, orange_star, orange_triangle, purple_circle, purple_diamond, red_circle, red_square, red_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, orange_triangle), (green_diamond, green_triangle), (green_hexagon, orange_circle), (green_square, red_square), (green_star, red_triangle), (orange_star, red_circle), (purple_circle, purple_diamond)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell068_seed00068004","image":"images/path_test_cell068_seed00068004.png","image_sha256":"cfe702a5a9c488f2fd3a5c2848d033783008c47292e6c7114e9058cab7cc50f3","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_hexagon, blue_square, green_square, orange_hexagon, orange_square, orange_star, purple_diamond, purple_hexagon, purple_square, red_triangle, yellow_circle, yellow_diamond, yellow_square}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, blue_square), (blue_hexagon, orange_hexagon), (green_square, purple_square), (orange_square, yellow_diamond), (orange_star, purple_hexagon), (purple_diamond, red_triangle), (yellow_circle, yellow_square)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell069_seed00069000","image":"images/path_test_cell069_seed00069000.png","image_sha256":"b60aa892dac1967be53850b5f48d370680ee1348bfb8cf9ef2d65a4b1d981b13","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_star, blue_triangle, green_circle, green_hexagon, green_triangle, orange_circle, orange_diamond, orange_star, red_hexagon, red_square, yellow_circle, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_star, green_circle), (blue_triangle, yellow_circle), (green_hexagon, orange_circle), (green_triangle, red_square), (orange_diamond, orange_star), (red_hexagon, yellow_star)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell069_seed00069001","image":"images/path_test_cell069_seed00069001.png","image_sha256":"9f72015f3bf44888735fc541c2b67a50fcb1774f9a7624109ada5230b73fbce4","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_hexagon, orange_diamond, orange_star, orange_triangle, purple_circle, purple_hexagon, red_diamond, yellow_diamond, yellow_hexagon, yellow_star, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, yellow_triangle), (blue_hexagon, purple_circle), (orange_diamond, red_diamond), (orange_star, orange_triangle), (purple_hexagon, yellow_hexagon), (yellow_diamond, yellow_star)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell069_seed00069002","image":"images/path_test_cell069_seed00069002.png","image_sha256":"1ab0dfd8949a8232e771b6c83b0563d2f9cb60b92c2015a92bfb6de3f2f38014","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_hexagon, blue_square, blue_star, blue_triangle, green_circle, green_star, orange_diamond, orange_square, purple_circle, purple_star, red_circle, red_diamond, red_hexagon, yellow_circle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_hexagon, blue_triangle), (blue_square, blue_star), (green_circle, red_diamond), (green_star, orange_square), (orange_diamond, yellow_circle), (purple_circle, red_circle), (purple_star, red_hexagon)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell069_seed00069003","image":"images/path_test_cell069_seed00069003.png","image_sha256":"6ea17fc74b610b8d031d73aa3e216d37a13075bb0bca0fd23aa1bd1ad9604c85","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_hexagon, blue_triangle, green_circle, green_diamond, green_hexagon, green_square, green_triangle, orange_diamond, purple_circle, red_hexagon, red_square, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_hexagon, orange_diamond), (blue_triangle, green_hexagon), (green_circle, green_diamond), (green_square, green_triangle), (purple_circle, yellow_star), (red_hexagon, red_square)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell069_seed00069004","image":"images/path_test_cell069_seed00069004.png","image_sha256":"2bb7e7cbbfc0eb4aa28fa3c2207c1894bb2408e5754484e422ef3b706b7bacd5","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_diamond, blue_square, green_circle, green_diamond, green_hexagon, green_triangle, orange_diamond, purple_diamond, purple_square, red_circle, red_diamond, yellow_diamond, yellow_square}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, purple_diamond), (blue_diamond, blue_square), (green_circle, orange_diamond), (green_diamond, green_hexagon), (green_triangle, purple_square), (red_circle, yellow_diamond), (red_diamond, yellow_square)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell070_seed00070000","image":"images/path_test_cell070_seed00070000.png","image_sha256":"98b9776d381b65d9f7a59b150166261e30b26fe063aac4319b50bb08329fcf7a","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_hexagon, blue_square, green_star, orange_hexagon, purple_circle, purple_hexagon, purple_triangle, red_square, red_star, yellow_diamond, yellow_square, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_hexagon, orange_hexagon), (blue_square, yellow_diamond), (green_star, yellow_square), (purple_circle, red_square), (purple_hexagon, red_star), (purple_triangle, yellow_triangle)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell070_seed00070001","image":"images/path_test_cell070_seed00070001.png","image_sha256":"7568252283c3022c2fdb7af466771b7cbb5e1d1c8df352001b7a7e3045c37615","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_diamond, blue_hexagon, blue_square, blue_star, green_diamond, green_hexagon, green_square, green_triangle, orange_square, purple_diamond, purple_square, red_square, red_star, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_diamond, blue_hexagon), (blue_square, orange_square), (blue_star, purple_diamond), (green_diamond, red_star), (green_hexagon, red_square), (green_square, yellow_triangle), (green_triangle, purple_square)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell070_seed00070002","image":"images/path_test_cell070_seed00070002.png","image_sha256":"22f0fb56c4021f92fd32b54909b46c517a0d7b8cba52fdbe320fa951c6477473","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_triangle, green_diamond, green_square, green_star, green_triangle, orange_diamond, orange_square, red_square, red_star, red_triangle, yellow_hexagon, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_triangle, green_triangle), (green_diamond, red_star), (green_square, red_triangle), (green_star, orange_diamond), (orange_square, yellow_star), (red_square, yellow_hexagon)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell070_seed00070003","image":"images/path_test_cell070_seed00070003.png","image_sha256":"b8cd9812927ad2469908771ed0aaeac26b4ae3910f77f5f014de048396ec0454","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {green_star, green_triangle, orange_circle, orange_square, orange_star, orange_triangle, purple_square, purple_star, red_hexagon, red_star, yellow_diamond, yellow_square}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(green_star, orange_square), (green_triangle, red_hexagon), (orange_circle, orange_star), (orange_triangle, yellow_diamond), (purple_square, yellow_square), (purple_star, red_star)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell070_seed00070004","image":"images/path_test_cell070_seed00070004.png","image_sha256":"a7b839f9e834136c9d028eb3d9eaf62b7b0a382d5c28b625163a15c8fb5ada78","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {green_circle, green_triangle, orange_square, orange_triangle, purple_square, purple_star, red_circle, red_diamond, red_hexagon, red_triangle, yellow_circle, yellow_hexagon, yellow_star, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(green_circle, orange_triangle), (green_triangle, red_diamond), (orange_square, yellow_circle), (purple_square, red_hexagon), (purple_star, red_circle), (red_triangle, yellow_triangle), (yellow_hexagon, yellow_star)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell071_seed00071000","image":"images/path_test_cell071_seed00071000.png","image_sha256":"c5006b78a39a11c5791cb088fff780b84b29a3e78c88abc5ece1fe015a3ce034","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_square, green_triangle, orange_circle, orange_diamond, orange_square, orange_star, orange_triangle, purple_circle, red_circle, red_diamond, red_square, yellow_circle, yellow_diamond, yellow_star}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_square, orange_circle), (green_triangle, orange_triangle), (orange_diamond, yellow_diamond), (orange_square, yellow_circle), (orange_star, red_diamond), (purple_circle, red_square), (red_circle, yellow_star)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell071_seed00071001","image":"images/path_test_cell071_seed00071001.png","image_sha256":"b7fc5a62f4d0d5cc0fa776ca80f3a4354814686de98f24999d936be87628a6c2","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_hexagon, blue_star, green_circle, green_square, purple_diamond, purple_hexagon, purple_square, purple_star, red_hexagon, yellow_circle, yellow_square}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, yellow_square), (blue_hexagon, green_square), (blue_star, yellow_circle), (green_circle, purple_diamond), (purple_hexagon, red_hexagon), (purple_square, purple_star)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell071_seed00071002","image":"images/path_test_cell071_seed00071002.png","image_sha256":"cb026f133a149fdcc2416db2c30be508e627f8f369e07495510225f024989d14","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_circle, blue_hexagon, blue_square, green_diamond, orange_hexagon, orange_star, purple_circle, purple_diamond, purple_hexagon, red_square, red_triangle, yellow_circle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_circle, orange_hexagon), (blue_hexagon, green_diamond), (blue_square, purple_circle), (orange_star, red_triangle), (purple_diamond, purple_hexagon), (red_square, yellow_circle)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell071_seed00071003","image":"images/path_test_cell071_seed00071003.png","image_sha256":"8ef4329ba0849d429362bef10b47194f8ea69b2c889584b4698dea04e57df49e","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {green_circle, orange_hexagon, orange_star, orange_triangle, purple_hexagon, purple_star, purple_triangle, red_diamond, red_hexagon, red_triangle, yellow_hexagon, yellow_triangle}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(green_circle, purple_star), (orange_hexagon, red_diamond), (orange_star, orange_triangle), (purple_hexagon, yellow_hexagon), (purple_triangle, yellow_triangle), (red_hexagon, red_triangle)}.","difficulty":"hard","endpoint_type":"shape"} | |
| {"sample_id":"path_test_cell071_seed00071004","image":"images/path_test_cell071_seed00071004.png","image_sha256":"8dcdffcd911e3953a519b152ff756dd1fa7121d9aafa1429abefec0aa2433136","question":"The image contains multiple curves, each connecting two endpoints in the image. The endpoints in this image are labeled: {blue_square, blue_triangle, green_hexagon, green_square, green_triangle, orange_hexagon, orange_square, purple_diamond, red_diamond, red_hexagon, yellow_hexagon, yellow_square}. Each label appears exactly once. Your task is to identify all connection pairs.\n\nTrace each curve carefully. Pay attention to crossings where lines overlap — at each crossing, the correct continuation should maintain smooth direction and curvature consistency. After completing all traces, verify your results to ensure they are consistent and correct.\n\nOutput the connection pairs in the format: \\boxed{(label_a, label_b), (label_c, label_d), ...}","answer":"Based on the traces above, the connection pairs are: \\boxed{(blue_square, green_hexagon), (blue_triangle, orange_hexagon), (green_square, red_hexagon), (green_triangle, orange_square), (purple_diamond, yellow_hexagon), (red_diamond, yellow_square)}.","difficulty":"hard","endpoint_type":"shape"} | |