
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
Given that in regular hexagon $ABCDEF$, points $M$, $N$, $O$, $P$, $Q$, and $R$ are chosen on sides $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, $\overline{DE}$, $\overline{EF}$, and $\overline{FA}$ respectively, so that lines $AM$, $NP$, $OQ$, and $FR$ are parallel and equally spaced, and the lines divide the height of the hexagon into four equal parts, find the ratio of the area of hexagon $MNPQRF$ to the area of hexagon $ABCDEF$.

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