Large language models (LLMs) have shown promise in psychological support, yet existing CBT-oriented systems often rely on prompt-based imitation or supervised learning from counseling-like responses, without explicitly modeling the structured therapeutic process of Cognitive Behavioral Therapy (CBT). This limits their controllability, intervention completeness, and coherence in multi-turn counseling. We formulate CBT-based psychological dialogue as a stage-aware controllable generation problem, where therapeutic stages serve as explicit control signals for intervention selection and therapeutic progression. To provide structured supervision under limited access to real counseling data, we design a CBT-stage multi-agent data generation engine that synthesizes multi-turn dialogues with user-state trajectories, stage-specific interventions, and content-level verification. Using the generated stage-structured data, we train Qixin, a CBT dialogue model that internalizes stage-aware therapeutic behaviors without requiring multi-agent coordination at inference time. We further introduce a hierarchical evaluation paradigm covering single-turn counseling skills, CBT procedural fidelity, stage alignment, and longitudinal session coherence. Experiments show that Qixin improves CBT-oriented counseling capability and outperforms existing psychological dialogue models and similarly sized open-source LLMs at the process level, achieving stronger procedural fidelity, stage consistency, and session-level coherence. These results demonstrate the effectiveness of explicit therapeutic-stage supervision for process-aware psychological support. Code and data are released.