\( \triangle ABC \) has an area of \( 240 \). Points \( X, Y, Z \) lie on sides \( AB, BC, \) and \( CA, \) respectively. Given that \( \frac{AX}{BX} = 3 \), \( \frac{BY}{CY} = 4 \), and \( \frac{CZ}{AZ} = 5 \), find the area of \( \triangle XYZ \).

Let's think step by step and output the final answer within \boxed{}.
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