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High-coverage hardware verification exemplifies this challenge due to its reliance on industrial simulators and non-differentiable execution signals. We propose LLM4Cov, an offline agent-learning framework that models verification as single-step state transitions guided by deterministic evaluators. Building on this formulation, we introduce execution-validated data curation, policy-aware agentic data synthesis, and worst-state-prioritized sampling to enable scalable learning under execution constraints. We further curate a reality-aligned benchmark adapted from an existing verification suite through a revised evaluation protocol. 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