If you can't remember your previous dream, that doesn't matter because that is just something that I naturally do and that is why I think about it. You can think about what ever you want, because the dream is just a vivid thought, sometimes I just visualise myself getting out of bed, it's the switch of consciousnes that is important to look for.
Do you mean that you don't fall asleep between the alarms? Anyway I used to do that too, but then I tried out different alarm setups, to find what suited me best.