en_tn_lite_do_not_use/act/18/04.md

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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.

trying to persuade both Jews and Greeks

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