
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
An isosceles triangle \( ABC \) with base \( AC \) is inscribed in a circle \(\Omega\). Chords \( DN \) and \( LT \), parallel to the line \( AC \), intersect the side \( BC \) at points \( F \) and \( H \) respectively, and \( BF = FH = HC \). Find the radius of the circle \(\Omega\) and the area of the triangle \( ABC \) if \( DN = 2 \sqrt{30} \), \( LT = 2 \sqrt{42} \), and the center \( O \) of the circle \(\Omega\) is located between the lines \( LT \) and \( AC \).

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