Meaning of “sympathize” - Learner’s Dictionary

sympathize

verb [ I ] ( also UK -ise) uk us /ˈsɪmpəθaɪz/
PROBLEMS

to understand and care about someone's problems:

It's a really bad situation - I do sympathize with her.
IDEAS

to agree with or support someone's ideas or actions:

I sympathize with the general aims of the party.

(Definition of “sympathize” from the Cambridge Learner’s Dictionary © Cambridge University Press)