
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 $\sqrt{50}$ cm, the length of $AB$ is $8$ cm, and that of $BC$ is $3$ cm. The angle $ABC$ is $45^\circ$. Find the square of the distance from $B$ to the center of the circle, assuming the situation can be described in coordinates with the circle centred at the origin $(0,0)$.

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