
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
On the extension of the side \(AC\) of triangle \(ABC\) beyond point \(A\), there is a point \(T\) such that \(\angle BAC = 2 \angle BTC\). Find the area of triangle \(ABC\), given that \(AB = AC\), \(BT = 70\), and \(AT = 37\).

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