
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
In regular octagon $ABCDEFGH$, points $I$, $J$, $K$, $L$, $M$, $N$, $O$, and $P$ are chosen on sides $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, $\overline{DE}$, $\overline{EF}$, $\overline{FG}$, $\overline{GH}$, and $\overline{HA}$ respectively, such that lines $AI$, $JP$, $KL$, and $MO$ are parallel and equally spaced, dividing the sides into three equal parts. What is the ratio of the area of octagon $IJKLMNOP$ to the area of octagon $ABCDEFGH$?
A) $\frac{1}{3}$
B) $\frac{5}{9}$
C) $\frac{4}{9}$
D) $\frac{2}{3}$
E) $\frac{11}{18}$

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