
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 quadrilateral $EFGH$, $m\angle F = 135^\circ, m\angle G = 135^\circ, EF=5, FG=7,$ and $GH=6.$ Find the area of $EFGH$.
A) $\frac{70\sqrt{2}}{4}$
B) $\frac{73\sqrt{2}}{4}$
C) $\frac{77\sqrt{2}}{4}$
D) $\frac{80\sqrt{2}}{4}$

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