You should be familiar with basic skills, important theorems, big ones and small ones. When you see this chart, you may think of some theorems that may be used in this chart.

Do more questions, previous questions, IMO simple questions, all the questions in several good books. If you do more, the inspiration for doing the problem will be faster and faster.

It is rare to find a very unconstrained auxiliary line. Therefore, when doing questions or exams, it is found that the auxiliary lines need to be continuously increased, and it is difficult to cut into the main points. Then 80% of the way is wrong. If the university has studied information theory or computational complexity theory, it will have a better understanding of this problem. In short, the auxiliary line is successful if it transforms a complex problem into a simple problem or transforms multiple variables into fewer variables. It is possible (but not absolute) to transform problems or variables in parallel and even increase the number of variables! ) is not a good choice.

Calculate less if you can. Most problems can't be solved in a daze, and so can non-proof problems. Even if you get the exam questions, you can see that it is feasible to be in a daze, but it is not good to delay too much time for the other two questions. It is worth trying other methods, especially in practice.

The high school competition has been too long. That's all I can think of for the time being. I hope it will help you a little.