
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 machine-shop cutting tool has the shape of a notched circle. The radius of the circle is 6 cm, and the lengths of segments $AB$ and $BC$ are 5 cm and 3 cm respectively. The angle $ABC$ is a right angle. Calculate the square of the distance from point $B$ to the center of the circle as well as the coordinates of $A$ and $C$ by assuming the center of the circle is at the origin.

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