In this work, we introduce a strategy that frames the sequential action selection problem for robots in terms of resolving \textit{blocking conditions}, i.e., situations that impede progress on an action en route to a goal. This strategy allows a robot to make one-at-a-time decisions that take in pertinent contextual information and swiftly adapt and react to current situations. We present a first instantiation of this strategy that combines a state-transition graph and a zero-shot Large Language Model (LLM). The state-transition graph tracks which previously attempted actions are currently blocked and which candidate actions may resolve existing blocking conditions. This information from the state-transition graph is used to automatically generate a prompt for the LLM, which then uses the given context and set of possible actions to select a single action to try next. This selection process is iterative, with each chosen and executed action further refining the state-transition graph, continuing until the agent either fulfills the goal or encounters a termination condition. We demonstrate the effectiveness of our approach by comparing it to various LLM and traditional task-planning methods in a testbed of simulation experiments. We discuss the implications of our work based on our results.