What type of action allows for the manual cycling of cartridges?

The correct answer is bolt action. Bolt action firearms utilize a manually operated mechanism where the shooter uses a handle to move a bolt that opens the breech, extracts the spent cartridge, and loads a new round into the chamber. This action provides the shooter with greater control over the cycling of cartridges, allowing for more deliberate shooting, which can be particularly beneficial in precision shooting scenarios.

In contrast, semi-automatic actions automatically cycle the next round after firing, requiring only a pull of the trigger for each shot, but do not involve manual cycling by the shooter. Muzzleloader actions require loading from the muzzle and have a different mechanism, and break actions involve a hinge that opens the barrel to load, but do not utilize a bolt mechanism. Thus, bolt action is the definitive type of action that directly allows for the manual cycling of cartridges.