
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
The base $MQ$ of trapezoid $MNPQ$ ($MQ \parallel NP, MQ > NP$) is the diameter of a circle which is tangent to line $MN$ at point $M$ and intersects side $PQ$ at point $K$. Additionally, $PQ = 4 \sqrt{3} KQ$. The radius of the circle is $R$, and $\angle NQM = 60^{\circ}$. Find the area of the trapezoid.

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