rely vs count

rely is not a noun while count is a noun.

Word	Noun	Adjective	Verb	Adverb
rely	No	No	Yes	No
count	Yes	No	Yes	No

As verbs, rely and count are synonyms defined as:

Other synonyms of rely include bank, bet, calculate, depend, look, reckon, swear.

rely (noun)	count (noun)
	the act of counting; reciting numbers in ascending order
	a nobleman (in various countries) having rank equal to a British earl
	the total number counted

rely (verb)	count (verb)
have faith or confidence in	include as if by counting
	have faith or confidence in
	take account of
	determine the number or amount of
	name or recite the numbers in ascending order
	show consideration for; take into account
	have weight; have import, carry weight
	put into a group
	have a certain value or carry a certain weight