$(X_{k})_{k }$ are IID, $P[X_{k}=1]=P[X_{k}=-1]=\frac{1}{2}$; $S_{n}=\sum_{k\leq n}X_{k}$ , $\tau=\inf\{n:S_{n}\in\{-a,b\}\}$. $E[\tau^{2}]=$?

Question

$S_{n}$ is martingale. Because $S_{n}^{2} -n$ is martingale, so we can get $E[S_{n\wedge\tau }^{2} -n\wedge\tau]=0$, we can get the $E[\tau]=E[S_{\tau}^{2}]=ab$. My question is $E[\tau^{2}]=$ ?. Because $S_{n}^{4}-6nS_{n}^{2}+3n^{2}+2n$ is martingale. I get the $E[S_{\tau}^{4}]-6E[\tau S_{\tau}^{2}]+3E[\tau^{2}]+2E[\tau]=0$. How can I calculate $E[\tau S_{\tau}^{2}]$ or calculate $E[\tau^{2}]$ directly by another method?