The isosceles right triangle \(ABC\) has a right angle at \(C\) and an area of \(12.5\). The rays trisecting \(\angle ACB\) intersect \(AB\) at \(D\) and \(E\). Find the area of \(\bigtriangleup CDE\). The original answer is in the form \(\frac{k - m\sqrt{n}}{p}\). Please provide the value of \(k + m + n + p\).

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