
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 dart board is shaped like a regular dodecagon divided into regions, with a square at its center. Suppose that a dart thrown at the board is equally likely to land anywhere on the board. What is the probability that the dart lands within the center square?
**A)** $\frac{2+\sqrt{3}}{6}$  
**B)** $\frac{\sqrt{3}}{6}$  
**C)** $\frac{2 - \sqrt{3}}{6}$  
**D)** $\frac{3 - 2\sqrt{3}}{6}$  
**E)** $\frac{2\sqrt{3} - 3}{6}$

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