There are two actuators, one is for the blend of cold to hot air, the other is the diverter from floor to vents to defrost.
If you adjust each dial (or push button setting if you have climate control) slowly, you can make the clicking start and stop. For me, my blend door will not go full cold, if it's cranked to full cold I get the clicking for about 30 seconds and then it gives up trying to move the blend door. However if I move the dial just one click up from full cold, no clicks and everything works fine. I can move from hot to cold and back with no issues as long as I never go full cold.
Once you figure out if it is the blend door or the diverter, we can help you replace the defective part.
The gears don't strip out inside the actuator, the big exposed drive spline either loses a tooth or the housing cracks allowing the gears to slip past one another. Never seen one where the gears inside stripped out.
This can also happen with the rear blend door in the same fashion, but the clicking will be from the rear obviously.