
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 \(A\), \(B\), \(C\), and \(D\) be points on a circle such that \(AB = 13\) and \(CD = 17\). Point \(P\) is on segment \(AB\) with \(AP = 7\), and \(Q\) is on segment \(CD\) with \(CQ = 9\). The line through \(P\) and \(Q\) intersects the circle at points \(X\) and \(Y\). If \(PQ = 25\), find \(XY\).

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