
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 octagon $ABCDEFGH$ has a smaller octagon formed by joining the midpoints of its sides. Determine the fraction of the area of the original octagon that is enclosed by the smaller octagon.

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