Explicit formula for $J[X,Y](f)$?

Question

Let $(M,J)$ be a complex manifold. I'm trying to find an explicit formula for $(J[X,Y])(f)$, like how for the simple commutator we have (by definition even) $$ [X,Y](f) = X(Y(f)) - Y(X(f)) $$ I'm trying to use the vanishing of the Nijehnuis tensor, which gives: $$ [X,Y] = [JX, JY] - J[JX,Y] - J[X,JY] $$ and so $$ J[X,Y] = J[JX, JY] + [JX, Y] + [X,JY] $$ But this doesn't seem to lead anywhere since I still have the $J[JX,JY]$ term.