Let $ABCD$ be a circumscribed quadrilateral such that $AD>\max\{AB,BC,CD\}$, $M$ be the common point of $AB$ and $CD$ and $N$ be the common point of $AC$ and $BD$. Show that \[90^{\circ}<m(\angle AND)<90^{\circ}+\frac{1}{2}m(\angle AMD).\] Fixed, thank you Luis.