en_tn_lite_do_not_use/act/18/04.md

So Paul reasoned

"So Paul debated" or "So Paul discussed." He gave reasons. This means that rather than just preaching, Paul talked and interacted with the people.

He persuaded both Jews and Greeks

Possible meanings are 1) "He caused both Jews and Greeks to believe" or 2) "He kept trying to persuade the Jews and the Greeks."