While large language models (LLMs) excel at open-ended dialogue, effective psychotherapy requires structured progression and adherence to clinical protocols, making the design of psychotherapist chatbots challenging. We investigate how different LLM-based designs shape perceived therapeutic dialogue in a chatbot grounded in the Self-Attachment Technique (SAT), a novel self-administered psychotherapy rooted in attachment theory. We compare three architectural variants: (1) a multi-agent system utilizing finite state machine aligned with therapeutic stages and a shared long-term memory, (2) a single-agent using identical knowledge-base and the same prompts, and (3) an unguided LLM. In an eight-day randomized controlled trial (RCT) with N=66 Farsi-speaking participants, balanced across the three chatbots, the multi-agent system is perceived as significantly more natural and human-like than the other variants and achieves higher ratings across most other metrics. These findings demonstrate that for therapeutic AI, architectural orchestration is as critical as prompt engineering in fostering natural, engaging dialogue.

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