For a triangle $XYZ$, we use $[XYZ]$ to denote its area. Let $ABCD$ be a square with side length $1$. Points $E$ and $F$ lie on $\overline {BC}$ and $\overline {CD}$, respectively, in such a way that $\angle EAF=45^\circ.$ If $[CEF]=1/19$, what is the value of $[AEF]$?

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