say vs asseverate

say is a noun but asseverate is not a noun.

Word	Noun	Adjective	Verb	Adverb
say	Yes	No	Yes	No
asseverate	No	No	Yes	No

As verbs, asseverate is a hypernym of say; that is, asseverate is a word with a broader meaning than say:

Other hypernyms of say include assert, maintain.

say (noun)	asseverate (noun)
the chance to speak

say (verb)	asseverate (verb)
express in words	state categorically
report or maintain
speak, pronounce, or utter in a certain way
express a supposition
give instructions to or direct somebody to do something with authority
communicate or express nonverbally
recite or repeat a fixed text
indicate
state as one's opinion or judgement; declare
utter aloud
have or contain a certain wording or form