ruminate
To think about something deeply again and again.
To ruminate means to think deeply about something over and over, turning it around in your mind like you're examining it from every angle. When you ruminate on a problem, you dwell on it, mulling it over and chewing on the idea repeatedly.
The word comes from what cows and other animals do when they chew their cud: they bring food back up from their stomach to chew it again and again. When you ruminate on an idea, you're doing something similar mentally, processing the same thoughts multiple times.
Sometimes ruminating helps you understand something better. A scientist might ruminate on a puzzling result until suddenly the answer becomes clear. A writer might ruminate on the perfect ending for her story. But ruminating can also mean worrying about something too much. If you keep ruminating on an embarrassing moment from last week, replaying it endlessly in your head, that's probably not helpful anymore.
The key difference between ruminating and regular thinking is the repetitive nature. You're returning to an idea again and again, sometimes productively and sometimes not, rather than simply considering it once and moving forward.