
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
Consider a regular dodecagon \(ABCDEFHIJKLMNOP\) with area \(n\). Let \(m\) be the area of quadrilateral \(ACEG\). What is \(\tfrac{m}{n}\)?
A) \(\frac{3\sqrt{3}}{9}\)
B) \(\frac{\sqrt{3} + 3}{3}\)
C) \(\frac{2\sqrt{3} + 3}{3}\)
D) \(\frac{2\sqrt{3} + 2}{3}\)
E) \(\frac{2\sqrt{3} + 3}{4}\)

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