In trapezoid $ABCD$, $AD\parallel BC$ and $AD:BC=1:2$. Point $F$ lies on $AB$ and point $E$ is on $CF$. If $S_{\triangle{AOF}}:S_{\triangle{DOE}}=1:3$ and $S_{\triangle{BEF}}=24$, find the area of $\triangle{AOF}$.
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