The escalating global demand for mental health services highlights the potential of Large Language Models (LLMs) in psychological counseling. However, current LLM-based approaches, particularly fine-tuned models, are constrained by data distribution biases, leading to limited therapeutic diversity and personalization. Crucially, they often lack anticipatory empathetic reasoning, struggling to foresee patient emotional responses beyond immediate dialogue history, and incur substantial computational costs. To address these limitations, we propose PsyPARSE, a novel training-free framework for psychological counseling that emulates the deliberate and empathetic reasoning of human counselors. PsyPARSE integrates Multi-Therapy Retrieval-Augmented Generation (RAG) to overcome data biases and provide highly personalized therapeutic approaches tailored to individual patient attributes. Pioneering the first multi-stage slow-thinking engine in mental health LLMs, PsyPARSE employs Multi-Turn Rollouts to identify optimal therapeutic paths and through anticipating patient reactions, optimizes empathetic responses, thereby ensuring genuinely empathetic and impactful responses in complex, long-dialogue interactions. Operating as a plug-and-play solution, PsyPARSE avoids the computational burden of fine-tuning. We establish a comprehensive LLM-based patient-therapist agent simulation framework for evaluation. Extensive experiments demonstrate that PsyPARSE significantly enhances the capabilities of various LLM baselines, achieving superior personalization and deeper empathy compared to both fine-tuned and other training-free methods. This work offers an efficient, adaptable, and scalable solution for advancing mental health support.