Synonyms for Assert (same or very similar meaning)
WordNet sense 1 (insist on having one's opinions and rights recognized):
put forward
WordNet sense 2 (state categorically):
asseverate, maintain
WordNet sense 3 (to declare or affirm solemnly and formally as true):
affirm, aver, avow, swan, swear, verify
WordNet sense 4 (assert to be true):
insist
From the ODE community, based on WordNet
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