
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 \(DE\) is a quarter-circle with center \(F\). The shaded region \(DEF\) is "rolled" along a straight board \(XY\) until it reaches its original orientation for the first time with point \(F\) landing at point \(F'\). If \(EF = \frac{3}{\pi}\) cm, what is the length of the path that point \(F\) travels?

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