In anomaly handling of nuclear operations, understanding safety-related outcomes requires more than observing whether a scenario is ultimately resolved. It also requires tracing how plant states are interpreted, how procedure logic is followed, which actions are selected, and how the system responds after each action. As AI-based operator support and autonomous decision-making technologies are increasingly explored in nuclear operation contexts, evaluating an AI agent only through final outcomes or isolated recommendations may obscure the procedural context and execution path behind its actions. To address this limitation, a graph-based procedure representation is used to encode procedure steps, branching logic, and execution context so that AI-selected actions can be traced within the procedural structure. This paper proposes a traceable AI-agent operation framework using graph-based procedures in a nuclear abnormal scenario simulation. The framework enables an AI agent to select candidate actions based on the current simulator state and procedure context, pass those actions through a constrained action space and validation layer, and record the resulting execution process as an action-level decision path. A prototype implementation demonstrates the feasibility of separating actions generated by an LLM-based decision module into accepted action sequences and rejected action attempts, with each action recorded together with its procedure step, validation result, rejection reason when applicable, and pre-action simulator state, as well as post-action simulator state when the action is accepted. The major outcome of the prototype is an action-level decision-path log that distinguishes accepted actions from rejected attempts and links each AI-selected action to procedure context, validation results, and simulator state transitions. A preliminary verification run illustrates that the proposed log can summarize accepted-action and rejected-attempt patterns while preserving the procedural context needed for future human-in-the-loop comparisons of human operator and AI-agent decision paths.