The coordinates of the vertices of rectangle $ABCD$ are $A(2, 3)$, $B(2, 7)$, $C(6, 7)$, and $D(6, 3)$. A point $P$ lies on the segment $AD$. Calculate the $60$th percentile of the $y$-coordinates of points $A$, $B$, $C$, $D$, and $P$. Use linear interpolation if necessary. Let's think step by step and output the final answer within \boxed{}.
user