In the realm of mental health support chatbots, it is vital to show empathy and encourage self-exploration to provide tailored solutions. However, current approaches tend to provide general insights or solutions without fully understanding the help-seeker's situation. Therefore, we propose PsyMix, a chatbot that integrates the analyses of the seeker's state from the perspective of a psychotherapy approach (Chain-of-Psychotherapies, CoP) before generating the response, and learns to incorporate the strength of various psychotherapies by fine-tuning on a mixture of CoPs. Through comprehensive evaluation, we found that PsyMix can outperform the ChatGPT baseline, and demonstrate a comparable level of empathy in its responses to that of human counselors.