
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 vertices of a regular octagon \(ABCDEFGH\) are joined to form a smaller octagon where each vertex of the smaller octagon is at the midpoint of the sides of the larger octagon. What fraction of the area of \(ABCDEFGH\) is enclosed by the smaller octagon?

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