The correct answer is C) slow to bare steerageway and navigate with caution. The International Regulations for Preventing Collisions at Sea (COLREGS) require that in heavy fog, when you hear the fog signal of another vessel ahead, you must slow to the minimum speed necessary to maintain steerage (bare steerageway) and navigate with extreme caution. This is to allow you to stop your vessel or take other action to avoid a collision if the other vessel is on a collision course. The other options are incorrect because maintaining speed or slowing only to a moderate speed would not provide the level of caution and control required in heavy fog when another vessel's location is unknown. Stopping the engines completely would also not be the appropriate action, as you need to maintain enough speed to retain steerage.