What is the addiction cycle?
I see it as.. commit a sin like having to much alcohol or drugs or other addictive thing.. feel bad for doing it.. and then ..
To get rid of the bad feeling... RETURNING to the alcohol or drug or other addictive thing.. to satiate the bad feeling.
Eg.. I drank too much last night.. I am feeling bad about it.. I am a twit! I can't handle this bad feeling.. what can I do? Oh there is more alcohol in fridge.. that will make me feel better..... back to the alcohol again. Cycle continues.
The Godly response to this is.. I had too much alcohol last night.. I am feeling bad.. and I am tempted to drink again.. but God has something better for me. I am sorry Jesus for turning to alcohol. Please forgive me. Thankyou for dieing on the cross for me and giving me eternal life. Your promises are better than this. You want me to flee sin.. not go after it.
The difference is guilt vs conviction.
Guilt.. doesn't normally lead to lasting change.. but CONVICTION from the Holy Spirit does.
The Godly response isn't too think about the sin.. but about Jesus and His promises. Thinking on the fruits of the Spirit rather than the addiction problem.
Problem here is your description of addiction as being a sinful act that sets it off. That may not always be the case. Caffeine isn't sinful, but it is addictive. That's just one example to make a point. There are others.
The next wrong assumption is that guilt over the act is the catalyst. Addiction cycles usually have a basis in something deeper emotionally. Or within the brain. And in some cases can even be physical.
So if a person drinks coffee (not a sin) every day to get moving, and becomes addicted and has trouble performing without it. And has physical affects, this addictive need has nothing to do with a sinful act.
There are various reasons for addiction. Guilt over an existing addiction may feed it, but not create the addiction