
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
In a modified design, a cutting tool has the shape of a notched circle. The radius of the circle is now 10 cm, and the straight segments are changed such that the length of \(AB\) is 8 cm and \(BC\) is 3 cm. The angle \(ABC\) is still a right angle. Find the square of the distance from \(B\) to the center of the circle. Assume the center of the circle is at the origin.

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