Final answer:
The serratus anterior is the muscle associated with the long thoracic nerve. It functions with the pectoralis minor to move the scapula, crucial for arm movements. The trapezius and sternocleidomastoid are innervated by the accessory nerve, which is different from the long thoracic nerve.
Step-by-step explanation:
The muscle that lies superficially with the long thoracic nerve is the serratus anterior. This muscle, along with the pectoralis minor, plays an important role in movements of the scapula (shoulder blade). The serratus anterior protracts and helps rotate the scapula, while the pectoralis minor stabilizes the scapula by drawing it anteriorly and downward against the thoracic wall. These actions are essential for the elevation and depression of the arm. The serratus anterior's close relationship with the long thoracic nerve is clinically important; damage to this nerve can lead to a condition known as 'winged scapula'.
The accessory nerve innervates other muscles associated with the scapula such as the sternocleidomastoid and trapezius, but it is not the nerve in question for the action described. It is important to distinguish between these muscles and nerves due to their separate functions and clinical implications.