
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 acute-angled triangle \(ABC\), heights \(AP\) and \(CQ\) are drawn from vertices \(A\) and \(C\) to sides \(BC\) and \(AB\), respectively. Given that the area of triangle \(ABC\) is 18, the area of triangle \(BPQ\) is 2, and \(PQ = 2\sqrt{2}\), find the radius of the circumcircle of triangle \(ABC\).

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