If an idea _____, you think about it for a short time.
cross your mind
to give someone a piece of advice that helps them do something
give someone a hint
to have an idea suddenly
have a thought
to change your opinion about something or start to doubt it
have second thoughts
to stop being able to think only about the thing you are doing
lose your concentration
to make a decision
make up your mind
to create ideas or pictures in your mind
use your imagination
