Large language models (LLMs) typically operate in a question-answering paradigm, where the quality of the input prompt critically affects the response. Automated Prompt Optimization (APO) aims to overcome the cognitive biases of manually crafted prompts and explore a broader prompt design space. However, existing APO methods often suffer from rigid template structures and inefficient exploration in the prompt space. To this end, we propose a Multi-Agent Adaptive Reasoning with Socratic guidance framework (MARS) for APO. MARS consists of five complementary agents and formulates the optimization process as a Partially Observable Markov Decision Process (POMDP), enabling adaptive prompt refinement through explicit state modeling and interactive feedback. Specifically, a Planner agent generates flexible optimization trajectories, a Teacher-Critic-Student triad engages in Socratic-style dialogue to iteratively optimize the prompt based on pseudo-gradient signals in the text space, and a Target agent executes the prompt in downstream tasks to provide performance feedback. MARS integrates reasoning, feedback, and state transition into a unified hidden-state evolution process, improving both the effectiveness and interpretability of optimization. Extensive experiments on multiple datasets demonstrate that MARS outperforms existing APO methods in terms of optimization performance, search efficiency, and interpretability.