
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 decagon $ABCDEFGHIJ$, points $K$, $L$, $M$, $N$, $O$, $P$, $Q$, $R$, and $S$ are selected on the sides $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, $\overline{DE}$, $\overline{EF}$, $\overline{FG}$, $\overline{GH}$, $\overline{HI}$, and $\overline{IJ}$ respectively. Each of these points divides their respective sides into segments with a ratio of 3:1, starting from the vertices $A$, $B$, $C$, $D$, $E$, $F$, $G$, $H$, $I$, $J$. Lines connected from alternate points as $KMOQSU$ create a new hexagon inside the decagon. What is the ratio of the area of hexagon $KMOQSU$ to the area of decagon $ABCDEFGHIJ$?
A) $\frac{1}{4}$
B) $\frac{3\sqrt{3}}{40}$
C) $\frac{9\sqrt{3}}{40}$
D) $\frac{1}{10}$

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