Your goal is to navigate a robot out of a maze. The robot starts in the center of the maze facing north. You can turn the robot to face north, east, south, or west. You can direct the robot to move forward a certain distance, although it will stop before hitting a wall. We can formulate this problem as follows. We'll define the coordinate system so that the center of the maze is at (0, 0), and the maze itself is a square from (-1, -1) to (1,1) Initial state: Robot at coordinate (0, 0), facing North. Successor function: Move forwards any distance d; change direction robot is facing. Cost function: Total distance moved. a) Let (x, y) be the current location. What is the Goal test? (2 points) b) How large is the state space? (2 points) For each of the following assertions, say whether it is true or false. Justify your answers. (6 points: 2 points each) a) Imagine the next Mars rover stops working upon arrival on Mars. From this we can deduce b) c) that Mars rover is not a rational agent. Every optimal search strategy is necessarily complete. Breadth-first search is optimal if the step cost is positive