Paraphrase for to solve a problem
Can I say work on it or work it out when I want to start to solve a problem, for example? The context is I have a friend who is looking for a someone to marry her, so I want to mean I'll start to help her to find someone.

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"Work on it" would be preferable.
"Work it out" is used more for a specific problem. For example:
"My wife and I don't really communicate like we used to. We're going to a marriage counselor to try to work out our problems/to try and work it out."