Let x, y, and z be positive real numbers that satisfy

2 \log _{x}(2 y)=2 \log _{2 x}(4 z)=\log _{2 x^{4}}(8 y z) \neq 0

The value of x y^{5} z can be expressed in the form \frac{1}{2^{p / q}}, where p and q are relatively prime positive integers. Find p+q.