Knowledge graphs (KGs) are often automatically constructed from large-scale corpora, but they inevitably contain factual errors due to noisy sources and extraction failures, and verifying them reliably at industrial scale remains a critical challenge. To address this, we propose AgentKGV, the Agentic LLM-RAG framework for KG fact Verification, that integrates dynamic routing and iterative query rewriting, which handles surface-form mismatch in document-level retrieval. To make this framework more accurate and cost-efficient for industrial deployment, we further introduce a two-stage training strategy: turn-level distillation-based SFT that transfers reasoning ability from a large teacher model into a small model for stable query rewriting and reasoning, and trajectory-level GRPO that optimizes the search policy to reduce unnecessary retrieval at scale. On the long-tail-predicate split of the open-domain T-REx benchmark, our framework improves macro-F1 over single-turn RAG by 5.5 \%p, and two-stage training does it further by 9.4 \%p. GRPO also cuts the average number of search calls from 3.24 to 1.63 without lowering accuracy.

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