I saw the BBC tweet some time ago, but I didn’t have time right at that moment to really think about a trio of songs that met the criteria. I have now, and mine are below. Please feel free to share yours! I’m all about crying/thinking/dancing (not necessarily in that order, but I feel like that’s the best order).
Leonard Cohen
Cry: Chelsea Hotel
Think: Ain’t No Cure for Love
Dance: Everybody Knows
Dylan
Cry: Ballad in Plain D
Think: Senor (Tales of Yankee Power)
Dance: Highway 61 Revisited
Depeche Mode
Cry: Somebody
Think: People are People
Dance: Dead of Night
Am I a music journalist yet 
Thanks. Interesting choices! Regards from Thom at the immortal jukebox (give it a spin!