
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 regular dodecagon (12-sided polygon) is labeled as $ABCDEFGHIJKL$. Let $n$ be the area of this dodecagon, and let $m$ be the area of quadrilateral $ACEG$. Determine the ratio $\tfrac{m}{n}$.
A) $\frac{1}{4}$
B) $\frac{1}{3\sqrt{3}}$
C) $\frac{\sqrt{3}}{4}$
D) $\frac{1}{6}$
E) $\frac{\sqrt{2}}{3}$

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