$Z_2^2$-actions with $n$-dimensional fixed point set

We describe the equivariant cobordism classification of smooth actions $(M^m,\Phi)$ of the group $G=Z_2^2$, considered as the group generated by two commuting involutions, on closed smooth $m$-dimensional manifolds $M^m$, for which the fixed point set of the action is a connected manifold of dimension $n$ and $m=4n-1$ or $4n-2$. For $m \ge 4n$, the classification is known.