
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
A circumcircle \(\Omega\) is drawn around an isosceles acute-angled triangle \(NPQ\) with base \(NQ\). Point \(F\) is the midpoint of the arc \(PN\) that does not contain point \(Q\). It is known that the distances from point \(F\) to the lines \(PN\) and \(QN\) are 5 and \(\frac{20}{3}\) respectively. Find the radius of the circumcircle \(\Omega\) and the area of the triangle \(NPQ\).

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