Mull (verb)

1. To ponder over or think deeply about something.
2. To consider something carefully and at length.
3. To heat and flavor (a beverage such as wine or cider) with spices and a piece of sugar or fruit.

Origin:

From middle english mulen, from old english mylan ("to grind, crush, rub"), from proto-germanic *mulijaną ("to grind, crush, rub"), from proto-indo-european *mel- ("to grind, crush").

Examples:

1. She mulled over the problem for hours before finally coming up with a solution.
2. He was mulling over whether or not to accept the job offer.
3. She was mulling the cider with cinnamon sticks and a slice of orange.
4. They were mulling the proposal before making a decision.
5. He was mulling the implications of the new policy.