Cue, as defined in Merriam Webster:
Definition of cue
a : a signal (such as a word, phrase, or bit of stage business) to a performer to begin a specific speech or action That last line is your cue to exit the stage.
b : something serving a comparable purpose : [HINT] I'll take that yawn as my cue to leave.
I feel CUE has the similar meaning as HINT in this case. Can we say:
That last line is your hint to exit the stage.
I'll take that yawn as my hint to leave.
I am not sure if these two words have some overlaps in meaning. Or sometimes they are interchangeable in some circumstances?