Verb[て] - Grammar Discussion

Thank you very very much for your reply.

If I have learned this issue incorrectly or incompletely, I would like you to correct me. I know that “てみる” is “used in situations where you are not sure whether you will be successful in doing an action.” am I wrong? and in the example I gave, I used “てみる” because I thought “let’s see if I can remember” the kanji I learned a few days ago (but I wasn’t sure about whether I could remember them correctly) and took action.

If I have chosen a wrong grammatical rule in this regard, I would like to learn the correct one from you.