(A) "give up" (III) → to quit or stop an activity, fits with deciding to stop dancing after an accident.
(B) "looks after" (IV) → to take care of someone/something, appropriate for caring for a pet dog.
(C) "roll out" (I) → to launch or introduce something new, commonly used for product releases.
(D) "ran out of" (II) → to exhaust the supply of something, makes sense for fuel during a long drive.
Hence, Option 1: (A) - (III), (B) - (IV), (C) - (I), (D) - (II) → Each phrasal verb naturally fits its sentence context: giving up an activity after injury, ensuring pet care, launching a product, and running out of fuel on a journey → correct