When performing reasoning tasks with user-specific requirements, such as strict output formats, large language models (LLMs) often prioritize reasoning over adherence to detailed instructions. Fine-tuning LLMs on supervised datasets to address this is impractical due to high computational costs and limited parameter access. To tackle this, we propose DICE, a lightweight framework that guides small language models (SLMs) to refine LLMs' outputs through chain-of-thought (CoT) correction. DICE decouples the process by first prompting LLMs to generate natural language responses, then using trained SLMs to analyze and refine these outputs to meet structured output specifications. This framework preserves LLMs' broad knowledge and reasoning capabilities while ensuring the outputs conform to user demands. Specifically, DICE first constructs structured CoT adaptation datasets via a two-stage method and subsequently applies a dual-tuning strategy to fine-tune SLMs for generating structured outputs in an analyze-then-answer pattern. Experiments demonstrate that DICE improves the average format accuracy and content correctness of LLM outputs by 35.4\% and 29.4\%, respectively, achieving state-of-the-art (SOTA) performance over other competitive baselines.