
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Let \(ABC\) be a triangle with \(AB = 13\), \(BC = 14\), and \(CA = 15\). Let \(D\) be the foot of the altitude from \(A\) to \(BC\). The inscribed circles of triangles \(ABD\) and \(ACD\) are tangent to \(AD\) at \(P\) and \(Q\), respectively, and are tangent to \(BC\) at \(X\) and \(Y\), respectively. Let \(PX\) and \(QY\) meet at \(Z\). Determine the area of triangle \(XYZ\).

Present the answer in LaTex format: \boxed{Your answer}
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