Here is a list of synonyms for the verb " assert"
advance, advocate, affirm, allege, allege in support, announce, annunciate, answer, argue, argue for, assever, asseverate, aver, avouch, avow, brook no denial, champion, confess, contend, contend for, counter, declare, defend, enunciate, espouse, express, express the belief, have, hold, insist, insist on, insist upon, issue a manifesto, lay down, maintain, make a plea, manifesto, nuncupate, persist, plead for, pose, posit, postulate, predicate, press, proclaim, profess, pronounce, propose, propound, protest, put, put it, quote, rebut, recite, refute, relate, reply, respond, riposte, say, say in defense, set down, set forth, speak, speak for, speak out, speak up, speak up for, stand for, stand on, stand up for, state, stick to, stick up for, submit, support, sustain, swear, take no denial, uphold, urge, urge reasons for, vow, warrant