Final answer:
The action of obturator externus is to laterally rotate the hip, and its nerve supply is the obturator nerve.
Step-by-step explanation:
The action of obturator externus is to laterally rotate the hip, not extend it. The correct answer is c) The action of obturator externus is to laterally rotate the hip.
The nerve supply of obturator externus is the obturator nerve, not the sciatic nerve. The correct answer is d) The nerve supply of obturator externus is the obturator nerve.
Therefore, the correct options are c) The action of obturator externus is to laterally rotate the hip and d) The nerve supply of obturator externus is the obturator nerve.