
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
Consider a regular octagon $ABCDEFGH$, where points $I$, $J$, $K$, and $L$ are respectively chosen on sides $\overline{BC}$, $\overline{DE}$, $\overline{FG}$, and $\overline{HA}$, such that lines $AB$, $IL$, $JK$, and $GH$ are parallel and equally spaced. Determine the ratio of the area of octagon $ICJKLGAI$ to the area of octagon $ABCDEFGH$.

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