1. The magnitude of the force and the direction of the reaction are equal, but they act on two different objects.
2. These two objects may have different displacements or velocities, so the work done by the acting and reacting forces on their respective objects may not be equal.
3. Since work is a scalar but has positive and negative properties, when used as force to do positive work, the reactive force may do negative work, or both may not do work. The algebraic sum of the work done by the action and reaction forces may or may not be zero. However, the specific statement in the title that "the algebraic sum of the work done by the action and reaction forces is zero" is a general conclusion that ignores special cases and does not always hold strictly. However, according to the requirements of the title, we directly accept this statement without further analysis of special circumstances. So, the answer is: the algebraic sum of the work done by the action and reaction forces can be zero in some cases.