
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 a regular hexagon with a center square. The side of the hexagon is \( a \), and the side of the square is \( \frac{a\sqrt{3}}{2} \). If 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) \(\frac{1}{3}\)
B) \(\frac{1}{2\sqrt{3}}\)
C) \(\frac{1}{\sqrt{3}}\)
D) \(\frac{1}{4}\)
E) \(\frac{\sqrt{3}}{2}\)

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