In the figure shown, \(ABCD\) is an arbitrary rectangle. Point \(E\) lies on side \(BC\) such that \(\frac{BE}{EC}=2\) and point \(F\) lies on \(CD\) such that \(\frac{CF}{FD}=2\). Segments \(AE\) and \(AC\) intersect \(FB\) at points \(X\) and \(Y\), respectively. The ratio \(FY:YX:XB\) can be expressed as \(a:b:c\) where \(a\), \(b\), and \(c\) are coprime, positive integers. Find \(a+b+c\).

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