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Computational psychiatry faces a fundamental trade-off: traditional reinforcement learning (RL) models offer interpretability but lack behavioral realism, while large language model (LLM) agents generate realistic behaviors but lack structural interpretability. We introduce BioLLMAgent, a novel hybrid framework that combines validated cognitive models with the generative capabilities of LLMs. The framework comprises three core components: (i) an Internal RL Engine for experience-driven value learning; (ii) an External LLM Shell for high-level cognitive strategies and therapeutic interventions; and (iii) a Decision Fusion Mechanism for integrating components via weighted utility. Comprehensive experiments on the Iowa Gambling Task (IGT) across six clinical and healthy datasets demonstrate that BioLLMAgent accurately reproduces human behavioral patterns while maintaining excellent parameter identifiability (correlations $>0.67$). Furthermore, the framework successfully simulates cognitive behavioral therapy (CBT) principles and reveals, through multi-agent dynamics, that community-wide educational interventions may outperform individual treatments. Validated across reward-punishment learning and temporal discounting tasks, BioLLMAgent provides a structurally interpretable "computational sandbox" for testing mechanistic hypotheses and intervention strategies in psychiatric research.