
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 circle of radius $3$ is cut into six congruent arcs. These arcs are rearranged to form a distinctive pattern that fits perfectly within a rectangle. If the length and width of the rectangle are $12$ and $6$ respectively, what is the ratio of the area of the new pattern to the area of the original circle?
A) $\frac{1}{2}$
B) $1$
C) $2$
D) $\frac{\pi}{2}$
E) $\frac{2}{\pi}$

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