
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
The whole arc of a circle with radius $R$ is divided into four large and four small parts, which alternate one after another. The large part is twice as long as the small part. Determine the area of the octagon whose vertices are the division points of the arc of the circle.

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