mull
To think carefully about something before deciding.
To mull something over means to think about it carefully and thoroughly, turning it around in your mind from different angles before making a decision. When your teacher asks if you want to join the debate team, you might need to mull it over for a few days, weighing whether you have enough time and whether you'd enjoy it.
The word suggests slow, thoughtful consideration rather than a quick decision. You wouldn't mull over what flavor of ice cream to order, but you might mull over which instrument to learn or whether to try out for the school play. When you're mulling, you're examining your options, imagining different outcomes, and letting your thoughts simmer.
People often mull things over while doing other activities: walking, doing chores, or lying in bed before going to sleep. Your brain keeps working on the question in the background. Parents mull over big family decisions, scientists mull over research questions, and writers mull over how to end their stories. The process of mulling helps you make better choices because you've given yourself time to think things through instead of just reacting on impulse.