
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 an isosceles trapezoid \(ABCD\) (\(BC \parallel AD\)), a circle of radius \(R\) is inscribed, touching the base \(AD\) at point \(P\) and intersecting segment \(BP\) at a point \(Q\) such that \(PQ = 3BQ\). Find the angles and the area of the trapezoid.

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