
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 $ABC$ with a right angle at $A$, the altitude $AH$ is drawn. A circle passing through 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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