
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 circle \(\Omega\) is circumscribed around an isosceles acute triangle \(C L E\) with base \(L E\). Point \(N\) is the midpoint of the arc \(C E\) that does not contain point \(L\). The distances from point \(N\) to the lines \(C E\) and \(E L\) are 6 and 9, respectively. Find the radius of the circle \(\Omega\) and the area of triangle \(C L E\).

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