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The LLM-as-a-judge paradigm uses large language models (LLMs) for automated text evaluation, assigning a score to the input based on scoring rubrics. Existing methods for fine-tuning LLM-as-a-judge use cross-entropy (CE) loss, which neglects the numeric nature of score prediction. Recent work addresses numerical prediction limitations of LLM fine-tuning through regression-aware fine-tuning but does not consider chain-of-thought (CoT) reasoning for score prediction. In this paper, we introduce TRACT (Two-stage Regression-Aware fine-tuning with CoT), which combines CoT reasoning with regression-aware training. TRACT uses a two-stage process: first, it fine-tunes the seed LLM to generate CoTs, which serve as the training data for the second stage; next, it uses these self-generated CoTs to retrain the seed LLM. The fine-tuning objective of TRACT applies CE loss for CoT reasoning and regression-aware loss for the score. Experiments across four LLM-as-a-judge datasets and two LLMs show that TRACT significantly outperforms existing methods. Extensive ablation studies validate the effectiveness of each component in TRACT.