The good news is, you don't have to play a shot in which your stance or swing is interfered with by an artificial cartpath. The rules permit you to drop within one club-length of the nearest point of relief that allows you to stand and swing freely without interference from the path (Rule 24-2, immovable obstruction). The nearest point and drop zone can't be closer to the hole, and it's recommended that the spot be determined by using the club, stance, direction and swing you would have used if the obstruction had not been there.
Sounds simple, but keep in mind the drop zone could be in a different place depending on whether you intend to swing left-handed or right-handed. Consult the diagram (above) for help understanding where to drop.
A player is entitled to relief without penalty from any path to which a foreign material (e.g., tar, gravel, dirt) has been applied. A player would not get relief from a dirt path created by vehicle traffic unless it had been defined as ground under repair.