I'm about to take a degree in Linguistics and Japanese. I want to explain my thought that linguistics supplements Japanese, and Japanese supplements linguistics. Is there a single verb that implies two entities support each other in this way? "Symbiotic" is a useful adjective, but it's not quite appropriate, because it suggests that the two entities depend on one another for survival. I'm merely trying to express that the two entities enhance or add to one another in some way. I was thinking that a verb like "cosupplement" and "cosupport" would work, but they don't appear to exist as words.
Linguistics and Japanese [mutually add to/supplement] one another.
A noun that refers to two entities adding to one another would also work nicely, as in:
Linguistics and Japanese are [mutually supplementary].