assert · verb /əˈsɜːt/
C1 T to say that something is certainly true
He asserts that she stole money from him.
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)
C2 to behave or speak in a strong, confident way
She has to learn to assert herself.
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
She soon asserted her authority as leader.
He can assert his authority over all the boys who are there. (Certificate of Proficiency in English; C2; Italian)