Harris would argue that even that capacity for self-reflection is just part of a very long causal chain. Every thought you have emerges from somewhere, but it's very hard to find the cause of that thought. You might be able to pin down that "I was thinking X because I was reminded by Y," but that just begs the question, why were you reminded by Y? There are an infinite number of thoughts you could have been having at that moment, but for some inscrutable reason Y bubbled to the surface.
All that said, though I think free will is an illusion, in terms of day to day life it's more practical to act as if you have free will. I believe Sam Harris agrees. He is more concerned about the public policy implications, such as incarceration and rehabilitation.
I've often experienced what I like to call 'déjà-vous at scale'. Many times while re-watching a film or re-reading a book, I recognise that my mind, triggered by some apparently inconsequential detail, has spawned a series of thoughts identical to those I had first time around at that very point in the narrative. This has happened months, sometimes years apart. I'd be interested to know if this effect has been studied and what the conventional term for it is. Occam's razor would posit that I am simply experiencing déjà-vous from a moment ago, but the qualitive feeling is very different from the déjà-vous I am obviously familiar with.
All that said, though I think free will is an illusion, in terms of day to day life it's more practical to act as if you have free will. I believe Sam Harris agrees. He is more concerned about the public policy implications, such as incarceration and rehabilitation.