The Greek word for "repent" is "metanoia" (noun) and "matanoeo" (verb) you see as defined in the Strongs #3340, 3341: to think differently or afterwards, reconsider. After thought, change of mind. Repentance basically means a "change of mind" and the context must determine what is involved in this change of mind.
One shows they have repented by their works. Just like we show our faith by our works (James 2:18) but faith in essence is not these works. Acts 26:20 declares, "I preached that they should repent and turn to God and prove their repentance by their deeds." This is the fruit of repentance (Matthew 3:8), not the essence of repentance.
So you simply define repentance as "works" and still claim we are saved by "works"? When God saw their works, that they turned from their wicked way, then God "relented concerning the calamity which He had declared He would bring upon them." They showed by their works that they have truly repented. In Jonah 3:4, we see that Jonah told the people of Ninevah that the city of Ninevah would be overthrown in 40 days if they do not repent of their wickedness (Jonah 1:2). The people of Nineveh repented "changed their minds" at the preaching of Jonah, believed God, and "turned from their evil ways" - "fruit of repentance" (Jonah 3:5,10; Matthew 3:8). The content of their faith was believing that God would overthrow Nineveh if they did not turn from their wicked ways, *not trusting in Christ's finished work of redemption for salvation. Unfortunately, the city of Nineveh reverted within one generation to its old pagan ways (Nahum 3:7,8). Turning from their evil ways was the fruit of their repentance. If we do our best to turn from our evil ways (self-reformation), yet fail to place our faith in Christ as the only means of our salvation, are we saved? No.
2 Corinthians 12:21 lest, when I come again, my God will humble me among you, and I shall mourn for many who have sinned before and have not repented of the uncleanness, fornication, and lewdness which they have practiced. Does practicing sin represent the fruit of repentance? No. Galatians 5:19 - Now the works of the flesh are evident, which are: adultery, fornication, uncleanness, lewdness, 20 idolatry, sorcery, hatred, contentions, jealousies, outbursts of wrath, selfish ambitions, dissensions, heresies, 21 envy, murders, drunkenness, revelries, and the like; of which I tell you beforehand, just as I also told you in time past, that those who practice such things will not inherit the kingdom of God. These are the unrighteous, not the righteous (1 Corinthians 6:9-10).
No repentance = no salvation = no works/fruit of repentance/salvation. Repentance is not simply another work in a series of works in an effort to receive salvation by works, as you teach. When we repent in receiving salvation, we change our mind about our sinful position and need for Christ to save us and any form of self trust in works and the new direction of this change of mind is faith in Christ for salvation. No longer practicing sin (such were some of you - 1 Corinthians 6:11) and good works are the fruit of repentance/faith. 1 John 3:9 - No one who is born of God practices sin, because His seed abides in him; and he cannot sin, because he is born of God. So repentance/faith are not simply works that merit our salvation. Saved through faith is not saved by works (Ephesians 2:8,9) and through belief/faith, we are completely trusting in "Another's work," (Christ's finished work of redemption - 1 Corinthians 15:1-4; Romans 1:16). Jesus Christ is the all sufficient means of our salvation. No supplements needed. So good works do not help save us. We are saved FOR good works and not by good works (Ephesians 2:8-10).