Final answer:
The correct action is to begin CPR with chest compressions on an unresponsive adult who has occasional gasps and no definitive pulse after being pulled from the water.
Step-by-step explanation:
When assessing an unresponsive adult who has been pulled from the water and who shows only occasional gasps, no definitive pulse, and no severe life-threatening bleeding, the correct course of action is to begin CPR with chest compressions. This is because the person is showing signs of cardiac arrest, and CPR can maintain the flow of blood, especially oxygen to the brain, which is critical for the patient's survival. It is essential to apply the correct CPR technique, pressing on the sternum at a proper depth and rate to effectively pump blood. Untrained individuals should be cautious, as incorrect application of CPR can cause severe injuries to the patient.