Probability and inequalities

A point inside the circle $x^{2}+y^{2}=16$ is selected at random. Given the system of absolute value inequalities:

$2\sqrt{3}-2<|y+x|<2\sqrt{3}+2$

$2\sqrt{3}-2<|y-x|<2\sqrt{3}+2$ ,

what is the probability the coordinates of the point satisfy the system? Round your answer to 3 decimal places.