What action should the Referee take if Fencer X steps off the side of the strip during an advance-lunge attack but scores a valid touch?

When Fencer X steps off the side of the strip during an advance-lunge attack, the proper action for the referee is to disallow the touch and have Fencer X return to the original position. This is based on the fundamental rules of fencing that require the fencers to maintain their positions on the strip during active engagements. If a fencer steps off the strip while performing a valid attack, it constitutes an infraction because the conditions for a valid engagement are not met.

The integrity of the competition demands that fencers remain within the confines of the strip to ensure fairness and safety. Therefore, even if the touch was valid, the infraction of stepping off the strip takes precedence. This ensures that all touches are scored under the correct circumstances, maintaining the integrity of the bout and the adherence to the rules.

Other choices involve actions that wouldn't appropriately address the violation according to standard regulations, as they either overlook the infraction or fail to properly reset the conditions of the bout.