
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 regular decagon is formed by connecting three sequentially adjacent vertices of the decagon. Find the probability that all three sides of the triangle are also sides of the decagon.

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