Does muse word has present continuous tense?

Yes, MUSING

Example: Aha! I can see Leonardo walking in the park, with his brow furrowed in deep thought. I expect he is musing on some fantastic new invention he has in mind!

Conjugation: I am musing, you are musing, he/she/(it?) is musing, we are musing, they are musing.

Quite amusing, really!