= Solution
The endpoints are the two <classical turning point>[classical turning points], determined by $V(x)=E$. Since the potential is even, they are symmetric. For $0\leq E\leq1$, they lie in the linear part of the potential and satisfy $|x|/4=E$; for $E\geq1$, they lie in the outer part and satisfy $\sqrt{|x|}-1=E$. Hence
$$
\boxed{
(a,b)=
\begin{cases}
(-4E,4E),&0\leq E\leq1,\\
(-(E+1)^2,(E+1)^2),&E\geq1.
\end{cases}}
$$
The <two-turning-point WKB quantization condition> uses
$$
\boxed{n=0,1,2,\ldots.}
$$
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