
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
Let $EFGH$ be a trapezoid with $EF||GH$, $EF=13$, $FG=7$, $GH=21$, and $HE=9$. The bisectors of $\angle E$ and $\angle H$ intersect at $R$, and the bisectors of $\angle F$ and $\angle G$ intersect at $S$. What is the area of hexagon $EFRGHS$?
A) $17\sqrt{13}$
B) $19.5\sqrt{3}$
C) $19.5\sqrt{13}$
D) $21\sqrt{13}$

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