
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 the plane, a rhombus \(ABCD\) and two circles are constructed, circumscribed around triangles \(BCD\) and \(ABD\). Ray \(BA\) intersects the first circle at point \(P\) (different from \(B\)), and ray \(PD\) intersects the second circle at point \(Q\). It is known that \(PD = 1\) and \(DQ = 2 + \sqrt{3}\). Find the area of the rhombus.

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