newtonian mechanics - Is there a reaction force for a reaction force?

According to Newton's third law of motion, for every action there an equal and opposite reaction.

If an object A applies a force (action) on an object B, object B applies an equal and opposite force (reaction) on object A. If we consider this reaction force as the action force applied by object B on object A, shouldn't there be a reaction force for every reaction force and hence infinite reaction forces?