
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
Regular dodecagon (12-sided polygon) $ABCDEFGHIJKL$ has area $P$. Diagonals $AC$, $CE$, $EG$, $GI$, $IK$, and $KA$ form a regular hexagon inside the dodecagon. Let $Q$ represent the area of this hexagon. What is the ratio $\frac{Q}{P}$?
A) $\frac{2 - \sqrt{3}}{2}$ 
B) $\frac{2\sqrt{3} - 3}{2}$
C) $\frac{3}{4}$
D) $\frac{3\sqrt{3}}{4}$
E) $\frac{3 - 2\sqrt{3}}{2}$

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