
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 hexadecagon divided into regions as shown in the layout. Suppose a dart thrown at the board is equally likely to land anywhere. Calculate the probability that the dart lands within the center square.

The hexadecagon is constructed in such a way that each vertex is connected to its fourth neighbor to form the center square, which divides the remaining segments into triangles.
A) $\frac{1}{16}$
B) $\frac{1}{9}$
C) $\frac{1}{8}$
D) $\frac{1}{10}$

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