Suppose $C$ is a category with a $\mathfrak{g}$-action, where $\mathfrak{g}$ is a semisimple Lie algebra. Then the Rickard complexes constructed by Chuang and Rouquier, one for each simple root of $\mathfrak{g}$, act as equivalences on the derived category $D^b(C)$. These complexes satisfy the braid relations for $\mathfrak{g}$, as shown by Cautis and Kamnitzer, and hence give a braid group action. We show that the complex corresponding to the positive lift of the longest Weyl group element (of any parabolic in $\mathfrak{g}$) is a perverse equivalence on $D^b(C)$. Hence, it induces a bijection on the irreducible objects of $C$, and recovers the cactus group action on a $\mathfrak{g}$-crystal. This is joint work in progress with Tony Licata, Ivan Losev, and Oded Yacobi.