
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 the right triangle \( ABC \) with the right angle at \( A \), an altitude \( AH \) is drawn. The circle passing through the points \( A \) and \( H \) intersects the legs \( AB \) and \( AC \) at points \( X \) and \( Y \) respectively. Find the length of segment \( AC \), given that \( AX = 5 \), \( AY = 6 \), and \( AB = 9 \).

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