The nine hidden words are:
     DASHER
     DANCER
     PRANCER
     VIXEN
     COMET
     CUPID
     DONNER
     BLITZEN
     RUDOLPH

The diagrams below show the letter tiles used for each phrase. The path begins with the magenta-circled letter.

DASHER
     

DANCER
     

PRANCER
     

VIXEN
     

COMET
     

CUPID
     

DONNER
     

BLITZEN
     

RUDOLPH
     

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