Since an Action class is a regular Java class that has a constructor, there's nothing to prevent you from instantiating an Action class and calling one of its methods from another Action class.
I would consider this to be very bad form, however. If you find yourself needing to do this, it's a good indication that it's time to refactor. Extract the logic that needs to be performed by both actions into a method in either a utility class or a business layer class and call the method from both Action classes.
You can also "chain" the actions with a forward with a path to the action (with the .do at the end). I've used this some times and it works well for me. Then in that action return ActionFoward to the another action.