Question 13
Let the focus and directrix of parabola $y^2 = 2px$ ($p \gt 0$) be $F$ and $l$, respectively. $A$ and $B$ are moving points on the parabola satisfying $\angle AFB = \frac{\pi}{3}$. Let the projection of $M$, the midpoint of segment $AB$, on $l$ be $N$. Then the maximum value of $\frac{|MN|}{|AB|}$ is ______.