The above contains a misunderstanding of Dennett. Intentionality and Intending are not the same thing.
This question curiously assumes that automatic processes are not mental actions. I don't see why such a position should have to be held. After all, having a certain desire might not be something someone does intentionally, but the propositional attitude "desires that" could certainly be counted among someone's mental states. Having a belief that it is raining when one is standing in the rain does not seem to be voluntary, but having the propositional attitude of believing that it is raining is no less a mental state, and having a desire to remain dry doesn't seem like something we have to expend any mental effort to conjure up, and having the belief that we have an umbrella, and having a belief that opening the umbrella will keep us dry are similarly devoid of any special mental effort, yet they all explain why we, of our own free will (that is, intentionally) open the umbrella. If any of Dennett's work is relevant to this part of the question, it is his work in compatibilism.
Additionally, there is a question of whether all cases of remembering have the same phenomenological flavor. Certainly in my own experience (and I would expect it to be similar to others) sometimes memories pop wholly unbidden to my notice, and these seem like unintentional happenings if anything my mind does is unintentional. However, sometimes I expend a great deal of effort to remember certain things, sometimes even going through old notes, or using mnemonic devices, or trying to remember related things, or asking other persons about what I'm trying to remember. This is an intentional action if anything I do is intentional.
See the sources on my other answer, this will help you get clearer about what you're looking for.