The famous 'four-chord trick', C Am F G. And if a writer was really ambitious the F would be replaced with Dm.
Yes, in my mind F is related to Dm. The C Am Dm G sequence has been used for decades with tunes like Heart and Soul, Blue Moon going back to the 30's and used as a vamp, intro, etc. And it is the basic turnaround. Nothing new at all IMHO
