
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 13. Circle \(\omega\) has radius 14 and its center \(P\) lies on the boundary of circle \(\Omega\). Points \(A\) and \(B\) lie on \(\Omega\) such that chord \(AB\) has length 24 and is tangent to \(\omega\) at point \(T\). Find \(AT \cdot BT\).

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