For convenience we shall assume that $B=f(U)$ where $U$ is as in Theorem 4.6. We can think of the above normalization as providing $U$ with canonical coordinates and $B\cong D^{2}\times D^{1}$ with coordinates $b_{1},b_{2},b_{3}$ such that the Hamiltonian vector fields of $b_{i}\circ f|_{U}$ are linear. This linearization will be used to compute the action coordinates explicitly. This is crucial to understand the singularities of the affine structure in the base.