Deriving Schwarzian Action in SYK Theory

Question

I am trying to derive the Schwarzian action for the $q=4$ SYK model following "An introduction to the SYK model" by V. Rosenhaus. I understand that we have the solution $$G(\tau_1, \tau_2) = \frac{b {\rm sgn}(\tau_1-\tau_2)}{ J ^{2\Delta}} \frac{f^\prime (\tau_1) ^\Delta f^\prime(\tau_2)^\Delta}{\vert f(\tau_1)-f(\tau_2)\vert^{2\Delta}} .\tag{3.4}$$ My problem is deriving the expansion of $G$. Supposedly, we change coordinates from $(\tau_1, \tau_2)$ to $(\tau_+, \tau_-)$ where $\tau_+= \frac{\tau_1+\tau_2}{2}$ and $\tau_-=\tau_1-\tau_2$. Taylor expand around $\tau_+$ $$G(\tau_1, \tau_2) = \frac{b {\rm sgn}(\tau_1-\tau_2)}{ \vert J (\tau_1-\tau_2) \vert^{2\Delta}} \left(1+ \frac{\Delta}{6} (\tau_1-\tau_2)^2 {\rm Sch}(f(\tau_+), \tau_+)+ O(\tau_1-\tau_2)^3 \right) .\tag{3.5}$$ It would be appreciated if someone could help show how this expansion is done or point to a resource where this has been detailed.