
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 in the shape of a regular decagon (10-sided polygon) with a side length of 1 unit each, and there is a center square connecting the midpoints of every alternate side of the decagon. Suppose that a dart thrown at the dart board is equally likely to land anywhere on the board. What is the probability that the dart lands within the center square?
**A)** 0.045
**B)** 0.085
**C)** 0.125
**D)** 0.165
**E)** 0.205

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