Alice and Bob are playing a game of reverse dots and boxes. The rules are simple:
- The players take turns adding one horizontal or vertical line in one free spot on the grid (marked with light gray lines in the below image). Alice goes first.
- If a move completes a $1\times1$ box, the player gets one point and has to make another move. The player keeps making moves until they make a move which does not complete a $1\times1$ box.
- The game ends when all possible lines have been drawn.
- Since this is a reverse game, the player with the most points loses.
Which of the players can win the game played in the above grid? What strategy should they use?