ITMC 2026 Grade 7 National Preliminary sample-r1 Question 5

In the figure, $AB=18$, $BC=19$, $CA=17$. $D$ lies on $AB$, $E$ on $CA$, and $F$ on $DE$ such that $\angle DFB=\angle DBF$ and $\angle EFC=\angle ECF$. Find the perimeter of triangle $ADE$.