In his trial before King Herod Agrippa in Acts 26, Paul went out of his way to emphasize that "works worthy of repentance" flow from turning to God and not from our own determination to prove our repentance.
The last two uses of a repentance word in Acts make it clear that repentance implies, and leads to, behavior demonstrating that repentance. In defending his ministry before King Herod Agrippa, Paul explained that he preached a repentance that led to action:
Therefore, King Agrippa, I was not disobedient to the heavenly vision, but declared first to them of Damascus, at Jerusalem, and throughout all the country of Judea, and also to the Gentiles, that they should repent (metanoein) and turn to God, doing works worthy of repentance (metanoias).
Acts 26:19-20
The Greek construction of verse 20 has four coordinate parts. The indicative verb refers to Paul’s preaching–“I kept declaring” (apēngellon), an imperfect past verb that asserts that what follows was Paul’s consistent message to Jews and Gentiles alike, wherever he preached. Paul’s message is described by two infinitives, “to repent” (metanoein) and “to turn” (epistrephein), followed by a participial clause describing the results that occurred when Paul’s hearers heeded his message. Paul told people to repent and to turn to God. In this context, “to repent” can be read in its more restricted sense of merely changing one’s mind or attitude–that of rejection–towards God, because it is immediately followed by the other half of true repentance, which is “to turn” towards (epi) or “to return to” God. Indeed, the concept of the need to turn or return (epistrephein carries both meanings) “to” God, not just to turn from known sin toward human remedies (for instance, religious observances or philosophical ethics) is given extra emphasis in that the particle epi is used redundantly, first as a constructive prefix in the verb epi-strephein, then one word later as a preposition introducing God.
Paul then describes the expected result of a repentant mindset that turns to God in the participial phrase at the end of verse 20. A literal reading of this clause, in the original Greek word order, is “worthy of the repentance works doing.” The action of the clause is carried in an present participle, prassontas, from the verb prassō, “I do, practice, accomplish” also “implying what is done as a regular practice – i.e. a routine or habit.” This participle is a masculine plural, modifying the masculine plural nouns in verse 19 describing the people to whom Paul had been preaching (“those” (tois) in Damascus and other regions, and “the Gentiles”), not the infinitives earlier in verse 20. What these people would be doing if they had both repented and turned to God was works (erga) worthy of (axia + genitive) “the” repentance (tēs metanoias) they had professed. The words here are not difficult. “Works” uses the plural of the most straightforward for something done by effort–ergon, “work, task, employment; a deed, action; that which is wrought or made, a work.” The word translated “worthy”–the “of” comes from the use of the genitive form of “the repentance” following it–is “axios,” “worthy, worthy of, deserving, comparable, suitable” in the sense of “to weigh in, assigning the matching value,” therefore also “of like value, worth,’ befitting, congruous, corresponding” (Thayer), which appears to be exactly the sense used here.
The only part of this construction that is confusing to modern thinking–and also, likely, to King Herod Agrippa, who was used to the Jewish approach of earning righteousness by doing it–is the use of the definite article (tēs) before “repentance.” Paul was going to great lengths here to emphasize that he was not preaching that people should simply repent and start doing right things, as the Law defined rightness, in their own strength, in reliance on themselves, in the manner of the Pharisees, in order to prove their repentance to God. No, instead, what Paul was preaching was that people need to both repent of their old, self-reliant way and turn to God. The expected result of doing this will be that they will now start doing works corresponding to “the” repentance God has already granted them. These works come from God, not from their own determination to prove their repentance to God. Compare, Ephesians 2:8-10. Approaching repentance in the manner of the Pharisees simply doesn’t work, compare Luke 11:24-26, and Paul wanted the King to understand this.