HMMT 2025 U6

Let $\triangle ABC$ be an equilateral triangle. Point $D$ lies on segment $\overline{BC}$ such that $BD = 1$ and $DC = 4$ . Points $E$ and $F$ lie on rays $\overrightarrow{AC}$ and $\overrightarrow{AB}$ , respectively, such that $D$ is the midpoint of $\overline{EF}$ . Compute $EF$ .