Let $ABCDEF$ be a regular hexagon with side length $2$. Denote by $X$, $Y$, and $Z$ the midpoints of sides $\overline{AB}$, $\overline{CD}$, and $\overline{EF}$, respectively. What is the area of the convex hexagon whose interior is the intersection of the interiors of $△ACE$ and $△XYZ$?