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Give a complete problem formulation for each of the following (initial state, goal test, actions, path cost). Choose a formulation that is precise enough to be implemented. a. Using only four colors, you have to color a planar map in such a way that no two adjacent regions have the same color. b. You start with the sequence ABABAECCEC, or in general any sequence made from A, B, C, and E. You can transform this sequence using the following equalities: AC = E, AB = BC, BB = E, and Ex = x for any x. For example, ABBC can be transformed into AEC (using BB = E), and then AC (using Ex = x), and then E (using AC = E). Your goal is to produce the sequence E. c. A container ship is in port, loaded high with containers. There 13 rows of containers, each 13 containers wide and 5 containers tall. You control a crane that can move to any location above the ship, pick up the container under it, and move it onto the dock. You want the ship unloaded.