There are four points on a plane as shown. Points $A$ and $B$ are fixed points satisfying $AB=\sqrt{3}$. Points $P$ and $Q$ can move, as long as $AP=PQ=QB=1$. Let $S$ and $T$ be the area of $\triangle{APB}$ and $\triangle{PQB}$, respectively. Find the maximum value of $S^2+T^2$.