Think$^{2}$: Grounded Metacognitive Reasoning in Large Language Models

Large Language Models (LLMs) demonstrate strong reasoning performance, yet their ability to reliably monitor, diagnose, and correct their own errors remains limited. We introduce a psychologically grounded metacognitive framework that operationalizes Ann Brown's regulatory cycle (Planning, Monitoring, and Evaluation) as a structured prompting architecture, and study its integration within a lightweight dual-process MetaController for adaptive effort allocation. Across diverse reasoning and diagnostic benchmarks (GSM8K, CRUXEval, MBPP, AIME, CorrectBench, and TruthfulQA) using Llama-3 and Qwen-3 (8B), explicit regulatory structuring substantially improves error diagnosis and yields a threefold increase in successful self-correction. Blinded human evaluations over 580 query pairs show an 84% aggregate preference for trustworthiness and metacognitive self-awareness over standard and Chain-of-Thought baselines. Grounding LLM reasoning in established cognitive theory offers a principled path toward more transparent and diagnostically robust AI systems.