SEAMO 2027 - Paper F - SET 03 - Self-study Question 4

Triangle $ABC$ is isosceles with $AB=1$ and $\angle A=90^\circ$. Points $E$ and $F$ lie on $AC$ and $BC$, respectively, with $FE\perp BE$. Given $AE=2/5$, write the area of triangle $CEF$ as $m/n$, where $m,n$ are relatively prime positive integers. Find $m+n$.

Original source figure, with all mathematical labels retained.