The correct answer is A) switch to hand steering. When the autopilot is engaged and the vessel starts to deviate significantly from the intended course, the first action should be to switch to hand steering. This allows the operator to immediately take manual control of the vessel and make the necessary corrections to bring the ship back on course. Switching to hand steering is the standard operating procedure in this situation, as it gives the operator direct control over the vessel's steering. The other options are not the appropriate first step. Checking the weather adjustment or rudder adjustment settings (B and C) should only be done after switching to hand steering, as those adjustments can then be made as needed to maintain the desired course. Engaging the "trick wheel" (D) is not a standard procedure and could potentially make the situation worse if the operator is not familiar with that equipment.