Actions come from decisions which are thoughts
Not necessarily. There are a ton of actions that do not come from conscious thought at all. Like currently I'm breathing without sparing a thought about breathing in and out and I still do it. Also I'm typing and while I think about the ideas, concepts, sentences and words, I spare not a single conscious thought on which keys I should hit on the keyboard, in fact I'm actually typing faster than the time that my mind would take to go through the different letters in those words. I can't even follow the movement of the fingers consciously unless I slow it down significantly. I'm certainly not consciously supervising these processes and with respect to breathing might not even have consciously set them in motion to begin with. It is not my "will" that I perform the bodily functions that keep my body alive like having my heart beat and so on.
I do not object to that and don't interfere with it (most of the time) but those are actions that "I" (the entity comprising body and mind) perform, but that are all "body" and not "mind", it's not "me", the conscious agent supervising the body to write these lines.
The process of doing so might even be controlled by the "brain" though not the "mind", so just because "brain" and "mind" are assumed to occupy the same physical space they do not necessarily refer synonymously to the same concept.
That being said, just because there are lots of actions that I do not perform consciously, there are also a lot of actions that I do perform consciously, like "writing" these lines (not the mechanical, but the thought process).
But when do we choose our thoughts?
Similar problem. Yes and no. There are lots of thoughts that you don't chose, because your body is constantly "perceiving" but your mind isn't constantly "listening" to that, so a lot of thoughts are subroutines coming to the surface of the consciousness, because they've reached a threshold of importance to become "emotions" about which we then develop "thoughts". So we don't choose them our bodies chose them for us. That being said just because you can close your eyes and lets thoughts pop up and fade into obscurity, you still have the ability to hold on to a thought, to concentrate upon it, to query your brain for more perception and data about it, to investigate it's connections, reasons and implications. So just because not every thought is conscious again doesn't mean that none is. And despite the fact that our thoughts are limited by our experiences, our thoughts are still quite free to mix and match everything that we've stored in memory. So that we can technically even imagine things vividly that do not exist and even cannot exist. Like do do you have a problem conceiving thoughts of aliens, monsters, gods, teleportation, time travel and so on? Probably not, have you ever seen them in real life? Probably not. But it's not difficult to combine idk a human or animal shape with the constraints of a horror movie, meaning that it should look scary, so idk sharp and metallic (invokes feelings of getting hurt easily by it)? blood red (invokes feelings of being hurt already or being about to as the threat is still present)? Gooey (also not pleasant and might stick and cause illnesses)? Maybe moldy in color and texture (natural aversion because of rotten food)? Dark (so that you can't make out the details and don't know what's hidden)? Or bright (so that you can't see anything)? Or some Cherenkov effect (that looks both marvelous and scary when you think of it's origin)?
So even if we are no gods that could think of a thing that we can't think about, there's still a lot of freedom and possibility in our thoughts and we can to a degree focus our attention or listen to the static.
Some argue that free will is a fundamental component of experience.
Well yes, experience is conscious experience, you can perceive things subconsciously, but you can't experience them subconsciously otherwise the memory would just a a vague indistinct feeling that you can't really comprehend consciously.
But if it was a fundamental component of experience, how could it even be doubted? [...] We may not be able to doubt that we experience,
You can doubt a lot of things. Like optical illusions and so on can make you doubt your perception and experience, or eating and suddenly feeling less angry might make you doubt your emotion of anger and might make you contemplate where it's coming from rather than directly reacting to it.
But I'm not aware of a way to switch off your mind without switching it off completely. You know you can knock your mind out, with physical force or drugs so that you're in a state of unconsciousness but then "you" don't exist, your body is just vegetating, but as long as you exist you are aware of your existence, right? Like you might not be aware of your body but you're nonetheless aware of your mind.
And you can't really step outside of your mind. So can you really question your "self"?
Now the problem is that there is a connection between "me", everything occupying the physical space of my body, "me" the conscious mind that does the thinking, "me" the body that does the action and part of the thoughts and stores the memory, including the brain that is part of the body yet responsible for the technicalities of the mind/body interface and likely host to the mind, which is again me, which is host to an internal simulating unit and a will (to interact with the surrounding world) and if they are all interacting based on physical principles then this should be a human machine that connected inputs to outputs, meaning there is no place for a "me" in that picture, yet I am as certain as nothing else on earth that "I" do posses the ability to both act internally "thinking" and "externally" relatively free, that is constraint by the body, by the laws of nature, by my own experiences, but not in a predetermined way or one where things could only go one way, so for all intents and purposes yes, I would say that I do experience free will. But the thing is if that isn't it and things are predetermined than I could feel differently anyway, but this feeling would be the result of my environment, so for practical purposes it doesn't actually matter.