AMC 8 2018 Problem 20

In $\triangle ABC,$ a point $E$ is on $\overline{AB}$ with $AE=1$ and $EB=2.$ Point $D$ is on $\overline{AC}$ so that $\overline{DE} \parallel \overline{BC}$ and point $F$ is on $\overline{BC}$ so that $\overline{EF} \parallel \overline{AC}.$ What is the ratio of the area of $CDEF$ to the area of $\triangle ABC?$

$\textbf{(A) } \frac{4}{9} \textbf{(B) } \frac{1}{2} \textbf{(C) } \frac{5}{9} \textbf{(D) } \frac{3}{5} \textbf{(E) } \frac{2}{3}$