<p>Efficient and accurate responses to public inquiries are critical for digital government services. However, existing rule-based and retrieval-based systems struggle with vague, multidimensional queries grounded in extensive policy documents, while large language models (LLMs) remain prone to knowledge gaps, topic drift, and hallucination. To address these limitations, we propose PD-LLM, a system that establishes real-time bidirectional coupling between LLMs and government knowledge graphs (KGs) via chain-of-thought (CoT) reasoning. At each reasoning step, PD-LLM dynamically retrieves and integrates policy facts, improving factual accuracy and coherence in multi-turn dialogues. Confidence-driven clarification and complexity-adaptive reasoning depth enable progressive transformation of vague user queries into structured entity queries, while quantitative stopping criteria ensure efficient termination upon information saturation. To enhance domain adaptability, the model employs two-stage fine-tuning on Qwen2.5-7B, strengthening its capacity to capture user intent, interpret policy content, and generate professional responses. Comprehensive automated evaluations demonstrate that PD-LLM consistently outperforms multiple baselines across n-gram precision, long-range dependency modeling, and semantic diversity. Dynamic KG injection further substantially reduces factual errors and authority overreach, yielding marked improvements in hallucination mitigation. These results confirm that integrating symbolic policy knowledge with stepwise LLM reasoning offers a practical and scalable solution for complex public service scenarios.</p>