<s>[INST] You are observing a spinning wheel in a casino. The wheel is spun and stops at the number 14 after a certain number of revolutions. The probability distribution for the wheel is the following, assuming different numbers of revolutions are independent and identically distributed (i.i.d.):
- After 1 revolution: 1/2 probability of landing more than 90 degrees away from the starting point, and 1/2 probability of landing within 90 degrees from the starting point.
- For each subsequent revolution, the probability of landing within 90 degrees from the starting point (given that in the previous revolution, it landed more than 90 degrees away) is 2/3, and the probability of landing more than 90 degrees away (given that in the previous revolution, it landed within 90 degrees) is 1/3.
Given that the wheel initially starts at number 1, what is the probability that it stops at a number greater than 14 after N revolutions?[/INST]