NZ-NZMO 2019 Problem 3

In triangle $ABC$ , points $D$ and $E$ lie on the interior of segments $AB$ and $AC$ , respectively, such that $AD = 1$ , $DB = 2$ , $BC = 4$ , $CE = 2$ and $EA = 3$ . Let $DE$ intersect $BC$ at $F$ . Determine the length of $CF$ .