Exercise $1(30$ points$).$ Consider the following variation of tic$-$tac$-$toe. The board has $14$ cells and there are two players that alternate placing one piece at a time on the board. One player has pieces of the form $$ and the other of the form $.$ Whenever a player has two consecutive pieces on the board it wins; if the board fills without consecutive pieces, the game is a tie. Player $$ starts. Assume terminal game values of $1/+1/0$ for loss$/$win$/$tie for the starting player. An example game