Large Language Models (LLMs) have shown great potential in supporting automated code review due to their impressive capabilities in context understanding and reasoning. However, these capabilities are still limited compared to human-level cognition because they are heavily influenced by the training data. Recent research has demonstrated significantly improved performance through fine-tuning LLMs with code review data. However, compared to human reviewers who often simultaneously analyze multiple dimensions of code review to better identify issues, the full potential of these methods is hampered by the limited or vague information used to fine-tune the models. This paper contributes MelcotCR, a chain-of-thought (COT) fine-tuning approach that trains LLMs with an impressive reasoning ability to analyze multiple dimensions of code review by harnessing long COT techniques to provide rich structured information. To address context loss and reasoning logic loss issues that frequently occur when LLMs process long COT prompts, we propose a solution that combines the Maximum Entropy (ME) modeling principle with pre-defined reasoning pathways in MelcotCR to enable more effective utilization of in-context knowledge within long COT prompts while strengthening the logical tightness of the reasoning process. Empirical evaluations on our curated MelcotCR dataset and the public CodeReviewer dataset reveal that a low-parameter base model, such as 14B Qwen2.5, fine-tuned with MelcotCR can surpass state-of-the-art methods in terms of the accuracy of detecting and describing code issues, with its performance remarkably on par with that of the 671B DeepSeek-R1 model.