
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 hexagon $ABCDEF$, lines $g$ and $h$ are drawn parallel to sides $\overline{AB}$ and $\overline{DE}$ respectively, where $g$ passes through the midpoint of $\overline{BC}$ and $h$ passes through the midpoint of $\overline{EF}$. Find the ratio of the area of quadrilateral formed by lines $g$ and $h$ and sides $\overline{CD}$ and $\overline{FA}$ to the area of hexagon $ABCDEF$.

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