suggest vs advocate

suggest is not a noun while advocate is a noun.

Word	Noun	Adjective	Verb	Adverb
suggest	No	No	Yes	No
advocate	Yes	No	Yes	No

As verbs, advocate is a hyponym of suggest; that is, advocate is a word with a more specific, narrower meaning than suggest:

suggest (noun)	advocate (noun)
	a person who pleads for a cause or propounds an idea
	a lawyer who pleads cases in court

suggest (verb)	advocate (verb)
make a proposal, declare a plan for something	push for something
call to mind	speak, plead, or argue in favor of
imply as a possibility
drop a hint; intimate by a hint