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Large language models (LLMs) have demonstrated significant reasoning capabilities in scientific discovery but struggle to bridge the gap to physical execution in wet-labs. In these irreversible environments, probabilistic hallucinations are not merely incorrect, but also cause equipment damage or experimental failure. To address this, we propose \textbf{BioProAgent}, a neuro-symbolic framework that anchors probabilistic planning in a deterministic Finite State Machine (FSM). We introduce a State-Augmented Planning mechanism that enforces a rigorous \textit{Design-Verify-Rectify} workflow, ensuring hardware compliance before execution. Furthermore, we address the context bottleneck inherent in complex device schemas by \textit{Semantic Symbol Grounding}, reducing token consumption by $\sim$6$\times$ through symbolic abstraction. In the extended BioProBench benchmark, BioProAgent achieves 95.6\% physical compliance (compared to 21.0\% for ReAct), demonstrating that neuro-symbolic constraints are essential for reliable autonomy in irreversible physical environments. \footnote{Code at https://github.com/YuyangSunshine/bioproagent and project at https://yuyangsunshine.github.io/BioPro-Project/ }

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