Step 1 (Recall definition of personification).
Personification is a figure of speech in which non-human things are given human characteristics or actions.
Step 2 (Identify the subject and action).
The subject "stars" is non-living and cannot literally perform human actions. The action "danced" is a human attribute.
Step 3 (Interpret meaning).
The sentence gives the stars a human action to create a vivid image, which is the hallmark of personification.
Step 4 (Verify with other options).
Not a simile (no "like" or "as" comparison), not a metaphor (no direct implied comparison), not hyperbole (not an exaggeration for emphasis).
\[
{\text{Personification (Option (c)}}
\]