
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 hexagonal dart board is divided into regions as shown below. 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 triangle?
The board consists of a large outer hexagon and a smaller equilateral triangle at its center, with lines extending from each vertex of the triangle to the nearest vertex of the hexagon.
Assume the side length of the hexagon is $s$.
A) $\frac{1}{3}$
B) $\frac{1}{6}$
C) $\frac{\sqrt{3}}{6}$
D) $\frac{\sqrt{3}}{3}$

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