Acceptance and Commitment Therapy (ACT) is a third-wave cognitive behavioral therapy with emerging evidence of efficacy in several psychiatric conditions. This study investigates the impact of post-training methodology and explicit reasoning on the ability of a small open-weight large language model (LLM) to deliver ACT. Using synthetic ACT transcripts generated by Mistral-Large, we trained Llama-3.2-3b-Instruct with two distinct approaches, supervised fine-tuning (SFT) and odds ratio policy optimization (ORPO), each with and without an explicit chain-of-thought (COT) reasoning step. Performance was evaluated by comparing these four post-trained variants against the base Instruct model. These models were benchmarked in simulated therapy sessions, with performance quantitatively assessed on the ACT Fidelity Measure (ACT-FM) and the Therapist Empathy Scale (TES) by an LLM judge that had been fine-tuned on human evaluations. Our findings demonstrate that the ORPO-trained models significantly outperformed both their SFT and Instruct counterparts on ACT fidelity ($χ^2(5) = 185.15, p < .001$) and therapeutic empathy ($χ^2(5) = 140.37, p < .001$). The effect of COT was conditional as it provided a significant benefit to SFT models, improving ACT-FM scores by an average of 2.68 points ($p < .001$), while offering no discernible advantage to the superior ORPO or instruct-tuned variants. We posit that the superiority of ORPO stems from its ability to learn the therapeutic `process' over imitating `content,' a key aspect of ACT, while COT acts as a necessary scaffold for models trained only via imitation. This study establishes that preference-aligned policy optimization can effectively instill ACT competencies in small LLMs, and that the utility of explicit reasoning is highly dependent on the underlying training paradigm.