In the diagram, points \(X, Y, Z\) are on the sides of triangle \(UVW\), as shown. Line segments \(UY, VZ, WX\) intersect at point \(P\). Point \(Y\) is on \(VW\) such that \(VY : YW = 4 : 3\). If triangle \(PYW\) has an area of \(30\) and triangle \(PZW\) has an area of \(35\), determine the area of triangle \(UXP\).

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