
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
Given that a dart thrown at a regular decagon is equally likely to land anywhere on the board, find the probability that the dart lands within the center pentagon formed by joining the midpoints of every second side of the decagon.

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