The correct answer is A) set out a kedge anchor. When a vessel runs aground, setting out a kedge anchor is the best initial action to take in waters with a falling tide. A kedge anchor helps to pull the vessel off the ground as the tide goes out, preventing further grounding and potential hull damage. The other options are less effective - slowly bringing the engine(s) astern (B) may not provide enough force to free the vessel, while shifting the load (C and D) does not directly address the grounding situation. Setting out a kedge anchor is the optimal choice to try and refloat the vessel before the tide fully recedes.