arXiv:2610.41738v1 Announce Type: new Abstract: Efficient agentic search requires large language models (LLMs) to determine whether they can reliably proceed with their current knowledge or need additional external evidence. Supervision based on final-answer correctness or trajectory-level feedback evaluates realized trajectory performance. However, observed trajectory performance is jointly shaped by stochastic generation, retrieval quality, and downstream reasoning. Such signals therefore provide only indirect evidence of how reliable the current decision state was and how retrieved evidence changed its reliability. An effective reward should encourage search when external information is needed and favor searches that contribute to the answer. To this end, we propose a metacognitive framework for training LLMs to make search decisions based on the reliability of their intermediate reasoning states. Our framework estimates the reliability of local conclusions to distinguish whether the current information supports proceeding without search from how much retrieved evidence improves that reliability. The current-state reliability score assesses whether the model can proceed without search. The search-action score measures how retrieved evidence changes estimated reliability. Together, these scores define a reliability-aware process reward for Group Relative Policy Optimization (GRPO), providing finer-grained supervision for search and no-search behavior. Experiments across seven question-answering benchmarks demonstrate that our method achieves a better accuracy-efficiency trade-off than strong agentic-search baselines. Our code and model checkpoints will be open-sourced.