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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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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 $M\\left(f_{n}\\right)$ be the minimum number of lines in a program that computes $f_{n}$, where each line computes either a disjunction or a conjunction. Prove that $M\\left(f_{n}\\right) \\geqslant M\\left(f_{n-2}\\right)+3$ for ... | 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{}. Two circles intersect at points \\( A \\) and \\( B \\) on the plane. Let \\( P Q \\) be one of their common tangents, with \\( P \\) and \\( Q \\) as the points of tangency. \\( S \\) is the intersection point of the tangents to the c... | 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.Nian is a monster which lives deep in the oceans. Once a year, it shows up on the land, devouring li... | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
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