Cross-domain task-oriented dialogue requires reasoning over implicit and explicit feasibility constraints while planning long-horizon, multi-turn actions. Large language models (LLMs) can infer such constraints but are unreliable over long horizons, while Reinforcement learning (RL) optimizes long-horizon behavior yet cannot recover constraints from raw dialogue. Naively coupling LLMs with RL is therefore brittle: unverified or unstructured LLM outputs can corrupt state representations and misguide policy learning. Motivated by this, we propose Verified LLM-Knowledge empowered RL (VLK-RL), a hybrid framework that makes LLM-derived constraint reasoning usable for RL. VLK-RL first elicits candidate constraints with an LLM and then verifies them via a dual-role cross-examination procedure to suppress hallucinations and cross-turn inconsistencies. The verified constraints are mapped into ontology-aligned slot-value representations, yielding a structured, constraint-aware state for RL policy optimization. Experiments across multiple benchmarks demonstrate that VLK-RL significantly improves generalization and robustness, outperforming strong single-model baselines on long-horizon tasks.