Large language models (LLMs) show promise in recommendation systems (RS), particularly when using Chain of Thought (CoT) reasoning. However, LLM hallucinations often make this reasoning unreliable. We propose TrackRec, a framework to enhance LLM reasoning for RS by accurately inferring a recommendation CoT (RecCoT) for user preferences. This RecCoT serves both as an explanation and as an auxiliary feature for recommendation tasks. TrackRec consists of a RecCoT generator (G) and a validator (V), which are trained using an alternating feedback learning mechanism. G is optimized via Direct Preference Optimization (DPO) using feedback from V to produce accurate RecCoT. Simultaneously, V is fine-tuned using inference feedback from G to improve its validation capabilities. This iterative process continuously improves both models. Extensive experiments show TrackRec surpasses state-of-the-art methods. It has been successfully deployed on a large-scale advertising platform with hundreds of millions of users, achieving substantial gains. We release the implementation at https://github.com/xiayu-cell/TrackRec .