In a first course on proofs in university, I received the following advice: start from the givens and try to get as close as you can to the proposition, as well

In a first course on proofs in university, I received the following advice: start from the givens and try to get as close as you can to the proposition, as well as start from the proposition and work backwards, trying to get as close to where you got earlier, and then hope that the two parts either meet in the middle, or are close enough to fool the examiner. This seems to work well enough for LLM's too.