preprint
<title>Abstract</title> Computational problem-solving often lacks effective verification processes, which introduces potential inaccuracies in problem-solving approaches. This research examines meta-cognitive methods for systematic problem-solving, emphasizing constraint realization, invariant property analysis, and solution verification. Drawing from recent advances in AI metacognition and cognitive problem-solving frameworks, we demonstrate the importance of systematic problem-solving protocols in eliminating cognitive biases and unverified claims to ensure correct solutions. The study introduces a structured verification model that integrates constraint realization, invariant property analysis, and systematic reasoning to enhance AI decision-making processes and reliability. Our experimental evaluation across leading AI models demonstrates significant variations in metacognitive problem-solving capabilities, with most models showing substantial improvement when guided by structured metacognitive prompts.
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DOI: 10.21203/rs.3.rs-6185693/v1
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