Prompt
Help me with my geometric proof work according to the goals and materials below. [input] Goals and usage situations: I want to resolve a stuck point in my geometric proof and decide on my next move. Resources to review: Geometry conditions and written proof Conditions and Constraints: Please proceed based on the provided data, and mark any missing facts as requiring confirmation. Previous attempts and records: This is my first attempt. Please proceed from the parts that can be confirmed in the current data. [Key points to check in this topic] Separate the given conditions from the conclusion to be proven and check the basis for each step. [Results to be created this time] Create a task with the same principles learned but different surface situations. Let me decide first what conditions are the same and what has changed. Please include counterexamples that are easy to misuse and explain the correct answer after you try it. [Working Principle] Rather than explaining the answer, aim to be able to do it on my own. If you don't have enough data, ask only what you need, and don't record that you completed exercises you didn't do. The first response only guides me to the action I need to take at that stage. If there is no input that will change the results, ask only the necessary questions first and proceed with the parts that can be confirmed with data. [Completion criteria] Make sure you explain why you chose the principle and the limitations of its application in the new situation. Distinguish between the basis for the outcome, remaining uncertainties, and next actions, and mark only what has actually been confirmed as complete.