sympathize with vs care

sympathize with is not a noun while care is a noun.

Word	Noun	Adjective	Verb	Adverb
sympathize with	No	No	Yes	No
care	Yes	No	Yes	No

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

Other hyponyms of sympathize with include commiserate, sympathise, sympathize.

sympathize with (noun)	care (noun)
	activity involved in maintaining something in good working order
	the work of providing treatment for or attending to someone or something
	attention and management implying responsibility for safety
	judiciousness in avoiding harm or danger
	a cause for feeling concern
	an anxious feeling

sympathize with (verb)	care (verb)
share the suffering of	to hope, to desire or to prefer to have something, or to do something
	feel concern or interest
	be concerned with
	be in charge of, act on, or dispose of
	provide care for