
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
A cutting tool is designed in the shape of a notched circle. The radius of the circle is $\sqrt{80}$ cm, with points $A$, $B$, and $C$ on its boundary such that $AB = 8$ cm and $BC = 3$ cm, forming a right angle at point $B$. Compute the square of the distance from $B$ to the center of the circle.

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