<image> Given two points A and B on the number line corresponding to the numbers -1 and 3 respectively, let point P be a moving point on the number line, corresponding to the number x.
(1) If the distances from point P to points A and B are equal, find the number corresponding to point P.
(2) Does there exist a point P on the number line such that the sum of the distances from point P to points A and B is 6? If it exists, find the value of x; if it does not exist, explain the reason.