assert · verb /əˈsɜːt/Full view
C1 T to say that something is certainly true
Dictionary example:

He asserts that she stole money from him.

Learner example:

Our department have already consulted [the] local Marketing Training Centre, which asserted that these employees are eligible to take the course. (Certificate in Advanced English; C1; Russian)

assert yourself
C2 to behave or speak in a strong, confident way
Dictionary example:

She has to learn to assert herself.

Learner example:

Such an attitude may also be the result of little pangs of homesickness or of our need to assert ourselves, to feel superior in a foreign country. (Certificate of Proficiency in English; C2; French)

assert your authority/control/independence, etc.
C2 to do something to show other people that you have power
Dictionary example:

She soon asserted her authority as leader.

Learner example:

He can assert his authority over all the boys who are there. (Certificate of Proficiency in English; C2; Italian)

Cambridge University Press