
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
The angle bisector of angle \( A \) of triangle \( ABC \) intersects side \( BC \) at point \( D \). A circle with radius 35, whose center lies on the line \( BC \), passes through points \( A \) and \( D \). It is known that \( AB^2 - AC^2 = 216 \), and the area of triangle \( ABC \) is \( 90 \sqrt{3} \). Find the radius of the circumcircle of triangle \( ABC \).

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