Prāyaścitta (atonement and repentance)

Namaskaram and Greetings to everyone here! As the title suggests, this post is about ***Prāyaścitta***, for our bad deeds. Many people of our faith argue that the concept of sin doesn't exist in our culture, I just believe that concept of sin is different in our culture from those in Abrahamic religion. While those religions focus more on blasphemous acts, our faith teaches us that any act committed against the calling of our atma/soul is a sin. Keeping in mind above view, I believe I have committed a few sins/bad deeds/acts which would generate me bad karma. While not the gravest or most serious of sins, they are surely some things I shouldn't have done. Like what? Like not following my duty of studying timely, not listening to my parents, fighting and shouting at them, consuming degenerate stuff from the internet, having degenerate thoughts and etc. I feel these are the sins not against anyone, but against my own being, my own soul. Yes I have hurt myself, indulging in behaviour which destroyed me and hurt those around me. Coming to the main point of this post, I want to repent for my sins. I searched wide across net and also this subreddit, the concept of Prāyaścitta has been suggested. Various methods like meditation, fasting, praying, donation, etc. have been suggested across various sources on internet. **But personally, I have been the kind of person who believes more in reforming from inside rather than external actions (karm-kaand)**. This does have a personal bias, because all through my life, I have seen the people who commit the most wrong deeds, like corruption, lying, decieving (a very good example can be of politicians, although i wasn't talking about them here in particular) are the ones who act to be very big devotees and believers. I simply don't understand, to explain it in a simple way, that how taking lord's name and offering prayers once in the evening, will wash away the abuses and swear words, the deceit and cheating you do through out the day. ***Hence, I wanted to ask that if genuinely asking for forgiveness from Lord Shri Ram and not repeating the same wrong behavior, along with following my god given duty, can be a way for Prāyaścitta?*** I just want to say sorry for my behavior and ask him to guide me to return to life of a good man. I plan on offering him a small prayer in my heart daily and following my duty everyday as a form of repentance, is that equal to doing prayers and donations?