According to dictionaries, "assert" means "to state categorically". Longman Dictinary of Contemporary English says:
(1) to state firmly that something is true
(2) assert your rights/independence etc. to state very strongly your right to do or have something
However, I don't understand what "assert" below means.
(3) the promise to assert more control over the army
In (3), "assert" does not seem to mean "state", but "use" or something like that. How should (3) be paraphrased?