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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": "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.Vanya wants to pass n exams and get the academic scholarship. He will get the scholarship if the ave... | 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{}. Prove that for every sufficiently large \\( n \\), in any set of \\( n \\) lines in general position, it is possible to color at least \\( \\sqrt{n} \\) of these lines blue such that no finite region from this set has a boundary entire... | 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{}. Arrange all simplest proper fractions with a denominator of 24 in ascending order, denoted as \\( \\left.a_{1}\\right) a_{2}, \\cdots, a_{n} \\). Determine the value of \\( \\sum_{i=1}^{n} \\cos \\left(a_{i} \\pi\\right) \\).\n\n(A) 1 ... | 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{}. The first $510$ positive integers are written on a blackboard: $1, 2, 3, ..., 510$ . An *operation* consists of of erasing two numbers whose sum is a prime number. What is the maximum number of operations in a row what can be done? ... | 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{}. There are triangles \\( A_{1} A_{2} A_{3} \\), \\( B_{1} B_{2} B_{3} \\), and \\( C_{1} C_{2} C_{3} \\) in a plane. Find a point \\( P \\) in the plane such that\n\n\\[ \\overline{PA_1}^2 + \\overline{PA_2}^2 + \\overline{PA_3}^2 = \\o... | 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{}. A triangle \\( ABC \\) is inscribed in a circle \\( O \\) and circumscribed around a circle \\( O' \\). Prove that if point \\( M \\) is the midpoint of the arc \\( AB \\) that does not contain point \\( C \\), then \\( MA = MB = MO' \... | 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 \\[g(x) = \\left\\{ \\begin{aligned} 3x+6 & \\quad \\text{ if } x < 0 \\\\ 2x - 13 & \\quad \\text{ if } x \\ge 0 \\end{aligned} \\right.\\]Find all solutions to the equation $g(x) = 3.$"
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"Your role as an assistant involves thoroughly exploring questions through a systematic long thinkin(...TRUNCATED) | [{"from":"user","value":"Return your final response within \\boxed{}. In triangle ABC, prove:\n$$\nx(...TRUNCATED) | 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 thinkin(...TRUNCATED) | [{"from":"user","value":"Generate an executable Python function generated from the given prompt. The(...TRUNCATED) | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
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