Wild Card Room

Lewis is trapped in a room with $4$ doors. He selects a door uniformly at random. Two of the doors have paths of lengths $5$ and $7$ miles that lead to freedom. The other two doors have paths of lengths $2$ and $4$ miles that lead back to the room Lewis is currently in. If Lewis selects a door uniformly at random in each step, find the expected amount of miles that he travels before reaching freedom?