Initially in the first box there are 1 black ball and 1 white ball and in the second box there is a white ball. Tom choose a ball randomly from the first box, put it into the second box, then choose a ball randomly from the second box and put it back to the first box. The above process is called a “round”. After the third round, the probability that the n two balls in the first box are of the different colors is (in the reduced fraction) . Find m the value of m + n .