sympathize vs empathize

sympathize and empathize both are verbs.

Word	Noun	Adjective	Verb	Adverb
sympathize	No	No	Yes	No
empathize	No	No	Yes	No

As verbs, sympathize and empathize are synonyms defined as:

Other synonyms of sympathize include empathise, sympathise, understand.

sympathize (verb)	empathize (verb)
be understanding of	be understanding of
to feel or express sympathy or compassion
share the feelings of; understand the sentiments of