You are given a train engine and three boxcars, which are all at the Chicago train station. There are two boxcars in Milwaukee. There is a train track connecting Minneapolis to Milwaukee, and one connecting Milwaukee to Chicago.

Your goal is to couple the five boxcars with the engine, move them all to Minneapolis, and take the engine back to Chicago.

You can couple a boxcar with an engine if they are both at the same train station. You can couple one boxcar at a time with an engine. You can connect as many boxcars as you want to an engine. Boxcars can be moved only if coupled with an engine. An engine can move from a station to another as long as there is a track connecting the stations, either directly or indirectly through another city.

Answer the following questions:

1. Define the action schemas for this train domain. Provide a description of the predicates you use sufficient to understand them unequivocally.

2. Define the initial state and the goal state.

3. Show a plan that can be obtained using your action schemas to accomplish the goal.