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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{}. Al gets the disease algebritis and must take one green pill and one pink pill each day for two weeks. A green pill costs $$$1$ more than a pink pill, and Al's pills cost a total of $\\textdollar 546$ for the two weeks. How much does on... | null | null | null | null | null | 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.Given a number and its reverse. Find that number raised to the power of its own reverse.\nNote: As a... | null | null | null | null | null | 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 $A\\in \\mathcal{M}_n(\\mathbb{R}^*)$ . If $A\\cdot\\ ^t A=I_n$ , prove that:\n\na) $|\\text{Tr}(A)|\\le n$ ;\n\nb)If $n$ is odd, then $\\det(A^2-I_n)=0$ ."
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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{}. For the older brother, the walk to school takes 12 minutes, while for the younger brother (along the same route), it takes 20 minutes. How many minutes will pass from the time the younger brother leaves home until he is caught up by th... | null | null | null | null | null | 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{}. Given two congruent triangles \\( A O B \\) and \\( A^{\\prime} O B^{\\prime} \\) (with a common vertex \\( O \\)), which do not lie in the same plane, prove that there exists a rotation of space around an axis that maps the first tria... | null | null | null | null | null | 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{}. For what value of \\(a\\) does the inequality \\(\\log \\frac{1}{\\div}\\left(\\sqrt{x^{2}+a x+5}+1\\right) \\cdot \\log _{5}\\left(x^{2}+a x+6\\right)+\\log _{a} 3 \\geqslant 0\\) have exactly one solution?"
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null | [{"from":"human","value":"Each vertex of convex pentagon $ABCDE$ is to be assigned a color. There ar(...TRUNCATED) | "Each vertex of convex pentagon $ABCDE$ is to be assigned a color. There are $6$ colors to choose fr(...TRUNCATED) | null | null | null | null | null | null | null | null | 1,163 | "To solve this problem, we need to consider the constraints given by the diagonals of the pentagon. (...TRUNCATED) | ["<think>\nOkay, so I have this problem here: Each vertex of a convex pentagon ABCDE is to be assign(...TRUNCATED) | [
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