
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
Circle \(\Omega\) has radius 5. Points \(A\) and \(B\) lie on \(\Omega\) such that chord \(AB\) has length 6. A unit circle \(\omega\) is tangent to chord \(AB\) at point \(T\). Given that \(\omega\) is also internally tangent to \(\Omega\), find \(AT \cdot BT\).

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