
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 a regular hexagon $ABCDEF$, points $G$, $H$, $I$, $J$, $K$, and $L$ are placed on sides $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, $\overline{DE}$, $\overline{EF}$, and $\overline{FA}$ respectively, such that lines $AG$, $KC$, $IL$, and $EH$ are parallel and divide each side into the ratio of $\frac{1}{4}$ and $\frac{3}{4}$. Determine the ratio of the area of hexagon $GHCIJK$ to the area of hexagon $ABCDEF$.
A) $\frac{1}{4}$
B) $\frac{27}{64}$
C) $\frac{9}{16}$
D) $\frac{27}{32}$
E) $\frac{9}{8}$

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