$ABCD$ is circumscribed in a circle $k$, such that $[ACB]=s$, $[ACD]=t$, $s<t$. Determine the smallest value of $\frac{4s^2+t^2}{5st}$ and when this minimum is achieved.
Problem
Source: 2022 Bulgarian Spring Math Competition, Problem 12.1
Tags: circumscribed quadrilateral, areas, geometry