Someone else (Neil Adler?) might be able to place it as being from an existing song.
It's a ii-V-I exercise, the new I becomes ii.
The bridge to Cherokee is like this, except it's C#m F# B, Bm E7 A, Am D G, Gm C Cm F
My progression resolves to the original tonality in C.
My feeling is that ii-V-I progressions proceeding to another a whole step down are a common jazz progression, e.g. How High the Moon.
Edit:Bluesette, duh!
Further edit—Climb Ev’ry Mountain