co-operates
coordinate
operate
Office.
hinder or oppose
exquisitely or masterpiece
task
its a pun, it means that there is no letter U in the word team but they also mean it as teams are not a selfish thing, you work together, the is more than just you in the team.
Magnificent. I think this is what you are looking for.
task
The root word for cooperation is "operate," which means to work together or function together in a joint effort or task.
A three-letter word that means "exist" is almost always "are." See if it will work.
The word cahoot can be very unique and creative. It means to be very excited and cheerful. It means to work together as a group as well. It is interesting.