Two particles move along the edges of equilateral $△ABC$ in the direction $A\Rightarrow B\Rightarrow C\Rightarrow A$, starting simultaneously and moving at the same speed. One starts at $B$, and the other starts at the midpoint of $\overline{CA}$. The midpoint of the line segment joining the two particles traces out a path that encloses a region $R$. What is the ratio of the area of $R$ to the area of $△ABC$?