
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
$ABCD$ is a rectangle; $P$ and $Q$ are the mid-points of $AB$ and $BC$ respectively. $AQ$ and $CP$ meet at $R$. If $AC = 6$ and $\angle ARC = 150^{\circ}$, find the area of $ABCD$.

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