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Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
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"value": "Return your final response within \\boxed{}. In a convex 100-sided polygon, any 3 diagonals do not intersect at an internal point. Prove that its 50 diagonals can divide the polygon into 1200 parts."
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"value": "<|begin_of_thought|>\n\nOkay, so... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
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"value": "Return your final response within \\boxed{}. Find the value of \\(10 \\cdot \\operatorname{ctg}(\\operatorname{arcctg} 3 + \\operatorname{arcctg} 7 + \\operatorname{arcctg} 13 + \\operatorname{arcctg} 21)\\)."
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Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
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"value": "Return your final response within \\boxed{}. Find all \\( n \\in \\mathbb{N}^{*} \\) such that \\( n \\) divides \\( 2^{n} - 1 \\)."
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"value": "<|begin_of_thought|>\n\nAlright, let's tackle this problem: Find all \\( n \\in \\mathbb{N}^{*} \\)... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
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"value": "Return your final response within \\boxed{}. Calculate \\((k+1)^{3} - k^{3}\\) then find the formula for \\(\\sum_{k=1}^{n} k^{2}\\)."
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"value": "<|begin_of_thought|>\n\nOkay, so I need to figure out the formula for the sum of squares from 1 t... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
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"value": "Return your final response within \\boxed{}. $S-ABCD$ is a regular quadrilateral pyramid. $P$ and $Q$ are the midpoints of $SB$ and $SD$, respectively. The plane passing through points $A$, $P$, and $Q$ divides $S-ABCD$ into two parts with volumes $V_1$ and $V_2$ ($V_1 < V_2$). F... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
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"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a string S of length N consisting of lowercase English letters.\nWe will cut this stri... | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
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"value": "Return your final response within \\boxed{}. Let $[x]$ represent the greatest integer less than or equal to $x$. Given that the natural number $n$ satisfies $\\left[\\frac{1}{15}\\right] + \\left[\\frac{2}{15}\\right] + \\left[\\frac{3}{15}\\right] + \\cdots + \\left[\\frac{n-1}{... | null | null | null | null | null | null | null | null | null | null |
"Your role as an assistant involves thoroughly exploring questions through a systematic long thinkin(...TRUNCATED) | [{"from":"user","value":"Return your final response within \\boxed{}. Let \\(ABC\\) be a triangle su(...TRUNCATED) | null | null | null | null | null | null | null | null | null | null |
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