For once, I haven't forgot to wear the little armband that comes with my sleep phase tracking alarm clock (I'll write a review of it soonish) and everything worked perfectly: I was woken up right after a dream (and thus REM phase) was ending, well-rested and alert.

This also made me remember the dream that I was seeing. Believe it or not, all I did in that dream was look at modern art at the Guggenheim museum (the one in New York).