Given that $x = x_1$ and $x = x_2$ are the local minimum and local maximum points respectively of the function $f(x) = 2a^x - ex^2$ ($a > 0$ and $a \neq 1$). If $x_1 < x_2$, then the range of $a$ is $\_\_\_\_$.
Given that $x = x_1$ and $x = x_2$ are the local minimum and local maximum points respectively of the function $f(x) = 2a^x - ex^2$ ($a > 0$ and $a \neq 1$). If $x_1 < x_2$, then the range of $a$ is $\_\_\_\_$.