
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
In a right triangle \(A B C\) with the right angle at \(A\), an altitude \(A H\) is drawn. A circle passing through points \(A\) and \(H\) intersects the legs \(A B\) and \(A C\) at points \(X\) and \(Y\) respectively. Find the length of segment \(A C\), given that \(A X = 5\), \(A Y = 6\), and \(A B = 9\).

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