The word you are looking for appears to be "asserts." In the context of an essay, "asserts" means to state a fact or belief confidently and forcefully. When an author asserts something in their writing, they are not merely suggesting or implying it; they are expressing it clearly and firmly as a truth.
The term "assert" originates from the Latin word "assertus," which is the past participle of "asserere," meaning "to affirm or claim." It is composed of "ad-" meaning "to" and "serere," meaning "to join together."