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In this work, we identify a primary bottleneck in informal theorem proving as a lack of insight, namely the difficulty of recognizing the core techniques required to solve complex problems. To address this, we propose $\\texttt{DeepInsight}$, a unified training framework designed to cultivate this essential reasoning skill and enable LLMs to perform insightful reasoning. 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To address this, we propose $\\texttt{DeepInsight}$, a unified training framework designed to cultivate this essential reasoning skill and enable LLMs to perform insightful reasoning. 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