\(ABC\) is a triangle with side lengths \(5,\) \(4\sqrt2,\) and \( 7.\)

Another triangle has side lengths \(\sin A,\) \(\sin B,\) and \( \sin C.\)

If the area of that triangle is \(\frac{p}{q},\) where \(p\) and \(q\) are coprime positive integers, then what is \(p+q?\)

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