Musing (verb)

1. To think deeply or ponder.
2. To consider something thoughtfully.

Origin:

From the middle english word "muse", meaning "to think deeply or ponder".

Examples:

1. He sat by the lake, musing on the nature of existence.
2. She spent the morning musing over her options for the future.
3. He was musing about how to solve the problem.
4. She was musing about the strange dream she had the night before.
5. He was musing on the beauty of the sunset.