Permutation Groups · Medium problem

In $S_4$, let $\sigma=(1\,2\,3)$ (so $1\to2\to3\to1$, $4\to4$). Suppose $\sigma\tau=(1\,4)(2\,3)$, where $xy$ means "apply $y$, then $x$". Using cancellation, solve for $\tau=\sigma^{-1}(1\,4)(2\,3)$ and state where $\tau$ sends $1$.