Final answer:
The first action when a vessel runs aground is to assess the situation to ensure safety and prevent further damage, followed by stopping all engines, checking for hull breaches, and evaluating the possibility of refloating.
Step-by-step explanation:
When a vessel runs aground, the first course of action is typically to assess the situation to prevent any further damage to the vessel and ensure the safety of everyone on board.
This includes stopping all engines to avoid exacerbating the vessel's predicament and checking for water intrusion or breaches in the hull.
After securing the immediate safety, the crew would likely perform a soundings and sightings check to determine the exact position and extent of grounding while also considering the state of the tide, the weather, and the potential for refloating. Salvage operations would commence afterward, sometimes requiring the application of torque to reorient the vessel, as illustrated by the challenge of calculating the necessary torque in a hypothetical situation.