You can act as if you are responsible for your actions, whilst knowing that you are not

The problem of free will goes much deeper than that, and none of what you said really applies. Your brain exists in the universe, and follows the laws of the universe, and physics are either deterministic or they're random. Interactions at the macro scale often follow deterministic behaviors. (Think billiard balls and such.) But then when you get down to the quantum scale, the results are truly random. Hell, the three-body problem is another situation that's truly random.

So where is the room for free will? It's obvious that your behaviors are based on things happening in your brain, and the things happening in your brain are just chemical reactions. Chemical reactions either do prescribed things or random things. How can your mind influence them?

Here's another philosophical angle. I first heard the idea from a classic philosorapter meme. "If we act based on our values, but don't choose our values, do we really have free will?"

(I had to recreate the meme. I couldn't find it.)

If you think about it, you never really choose your values. You feel them in your chest. They can change over time based on your lived experience, but no one sits down and says, "I'm going to choose be a social democrat". You might slowly come to the realization that it's the correct way to be, but you can't choose that any more than you can choose to be heterosexual or choose to enjoy eating smoked salmon. You have to feel it first. You don't choose your feelings. They're reactions to stimulus. Even fighting your impulses in order to do something else is itself driven by feelings.

The beauty of the brain is the strange loops and feedback mechanisms that allow you to analyze information. And some day, all of a sudden you realize your values were wrong and you change and grow, but there was no point where it was a choice.

Every action you take is dictated by impulses that you can't control. The impulse to eat, to fuck, to get out of the rain, or whatever. None of it is truly a choice. If you think it is, you can wind back the train of thought every time to find that it comes down to inherent values and impulses. Neither of which you choose.

Here's an example. Someone's having a really bad time and they're homeless maybe and addicted to drugs, and then someone comes along and says, "Just quit the drugs, and get a job and stop being homeless. I did it. So can you!" All that means is that that person at one point found the gumption to go through withdrawal and get their life back on track. But the thing is, they didn't choose to have the gumption. They just... had it. Or they had help. Either way, there was no choice involved.

For me, this conclusion that we don't have free will doesn't impact my personal life very much. It doesn't mean I can suddenly do whatever I want and blame my lack of free will. I do exactly what I was going to do anyway, based on my values and impulses. But it does help me forgive people who seem like they're total assholes. You know, criminals and such. When you can accept that people act based on impulses which they really can't control, then you can be more forgiving, and learn to love people as the flawed humans they are. I'm not saying it's easy. I'm not Christian, but that's the kind of love and acceptance that Jesus taught, and I believe it only comes if you abandon the idea of free will.

And the best way to help someone be better is talk to them, which affects how they think and gives them new perspectives. The only way anyone can change is to receive new input that changes their behavioral loops.

This is why I don't think any kind of criminal justice system should impose punitive sentences. If you need to sequester someone from society to protect others, then fine, but that sequestration shouldn't specifically be punishment, and I can't stand it when people make rape jokes about prison.

And why even bother being a better person if no one has free will and nothing really matters? Well, people have minds and feel pain, and I happen to value not causing people pain.

Then again, I'm also (internally) an asshole when people drive aggressively around me. I can't count how many times I've yelled out loud, "I hope you die in a fire!" when someone does a particularly dangerous maneuver and puts everyone else on the road at risk. That's not very forgiving of me. But I'm a flawed human just like everyone else, acting based on my impulses. ☹️