
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 $ABCD$, $m\angle B = m \angle C = 120^{\circ}, AB=5, BC=6,$ and $CD=7.$ Additionally, a diagonal $BD$ is drawn, with $BD = 8$, forming triangles $ABD$ and $BCD$. Find the area of $ABCD$.
A) $20.5\sqrt{3}$
B) $21\sqrt{3}$
C) $19.5\sqrt{3}$
D) $22.5\sqrt{3}$

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