
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 as a regular hexagon divided into regions, including a square at the center. Each side of the hexagon measures 2 units. Each vertex of the center square touches the midpoint of each side of the hexagon. Suppose 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) \( \frac{1\sqrt{3}}{3} \)
B) \( \frac{2}{3} \)
C) \( \frac{2\sqrt{3}}{3} \)
D) \( \frac{3\sqrt{3}}{3} \)

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