(2) Given the function $f(x)=\log _{a}\left(\log _{2 a} x-x^{2}\right)$ is defined for any $x \in\left(0, \frac{1}{2}\right)$, find the range of real number $a$.
(2) $a \in\left[\frac{1}{32}, \frac{1}{2}\right)$