When I hit bottom and first started real recovery, I made my priority doing whatever it takes to stay sober today. I wouldn't call it "working on my addiction", because for me, that puts too much power into my ego. After all, my addiction was really working on me. I did my part to live right: worked the steps with my sponsor, went to meetings regularly, and acted like I was really sick, cuz I am. And just doing that, made me change and slowly get healthier. I give all the credit for any improvement in myself to two things: (1) Hashem and, (2) l'havdil, my addiction. For me, it's like gravity: you get stronger and stronger just by walking around and not falling on your butt. But you have to be walking, not just standing there and "trying not to fall".
You can see how concentrating on "not acting out" can short-circuit the entire thing, because it's a sure way to keep me living in the problem, rather than in the solution.
In my case and others', the addict needed to give something up, to break free of the shame and admit the truth of their inability to stop - to themselves and to other (safe) people, and ask for help.
They also needed to stop doing what is not working for them. As long as they keep trying the same exact thing and expecting a completely different result (it'll work/I really mean it this time!), they are doomed to keep having taynos (complaints) on Hashem, thinking "why is He not helping me?!".
The things they are trying are:
1) Acting out (Yup! In the heat of the moment, we all figured that if we just gave in, the annoying tayva would finally leave us alone for a while, right?),
2) Davening for "help" (even though they are not letting go of the sheretz and doing nothing really different) - the SA white book calls this "begging G-d to take it away so that we do not have to give it up!"),
3) Learning/davening/doing every normal thing the same as we always have, as though nothing is wrong (hiding at all costs).
None of these things worked for me to quit, at all, and they only made the habit of living within the problem deeper and worse. (Sort of like not breaking the luchos, if you know what I mean. They were the luchos, after all... not very nice to throw luchos on the floor, you know....)
I am not saying davening does not help, nor am I suggesting we stop living normally. What I am talking about is admitting that our davening and learning, family time (or lack thereof), and other habits, have not been innocent bystanders in our problem. WE ARE one person. These good parts of our lives have most likely been molded and twisted, perverted, to allow us to live the sick way we have been living. They do not need to stop, but they need to change.