In the class, the professor emphasized the importance of writing a proof with all statements step-by-step. Please visit chat.deepseek.com and ask this AI a question about the main idea of the Chain of Thought (CoT) and the relationship between CoT and writing a proof with all statements step-by-step. When asking this question, please click "DeepThink (R1)" so that the model can return its "thought" before the answer.

For this problem, you need to 1) copy and paste your question and the answer you got from DeepSeek R1, and 2) take a screenshot and upload it to demonstrate the "thought" of DeepSeek before answering your question.