
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
Arc \(AC\) is a quarter-circle with center \(B\). The shaded region \(ABC\) is "rolled" along a straight board \(PQ\) until it reaches its original orientation for the first time with point \(B\) landing at point \(B'\). If \(BC = \frac{3}{\pi}\) cm, what is the length of the path that point \(B\) travels? Express your answer in simplest form.

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