
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 \(ABCD\) be a square of side length 5. A circle passing through \(A\) is tangent to segment \(CD\) at \(T\) and meets \(AB\) and \(AD\) again at \(X \neq A\) and \(Y \neq A\), respectively. Given that \(XY = 6\), compute \(AT\).

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