Large language models (LLMs) are promising tools for supporting security management tasks, such as incident response planning. However, their unreliability and tendency to hallucinate remain significant challenges. In this paper, we address these challenges by introducing a principled framework for using an LLM as decision support in security management. Our framework integrates the LLM in an iterative loop where it generates candidate actions that are checked for consistency with system constraints and lookahead predictions. When consistency is low, we abstain from the generated actions and instead collect external feedback, e.g., by evaluating actions in a digital twin. This feedback is then used to refine the candidate actions through in-context learning (ICL). We prove that this design allows to control the hallucination risk by tuning the consistency threshold. Moreover, we establish a bound on the regret of ICL under certain assumptions. To evaluate our framework, we apply it to an incident response use case where the goal is to generate a response and recovery plan based on system logs. Experiments on four public datasets show that our framework reduces recovery times by up to 30% compared to frontier LLMs.