Prompt
Help correct conceptual misunderstandings according to the goals and materials below. [input] Goals and usage situations: In Correcting Conceptual Misunderstandings, you want to resolve any stuck points and decide on your next course of action. Resources to review: Explain what I understand 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] Find the first premise that is off in my explanation and have them correct it themselves using counterexamples. [Results to be created this time] Please give me one task that I can solve at my current level. When I make a request or show a blocked part, I give hints one by one in the following order: direction, intermediate inspection, and core principles. Don't give complete answers all at once, but decide the next steps after each attempt. [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] Please separately record the steps you received a hint from and the steps you performed on your own. Distinguish between the basis for the outcome, remaining uncertainties, and next actions, and mark only what has actually been confirmed as complete.