Ruminate

While this verb can also mean "to chew over and over" (often used with cows and other similar animals), ruminate [roo-muh-neyt] has another definition I want to focus on this week: "to meditate or muse; ponder".  After a little rumination (see what I did there?), I came up with these sentences using the word:

Walking alone in the woods each morning 

gives me a chance to relax and ruminate.

Why don't you ruminate on those facts for awhile 

and try to come up with a solution to our problem?

How would you use the word ruminate?