
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 \( P Q T \) with a base \( P Q \) is inscribed in a circle \( \Omega \). Chords \( A B \) and \( C D \), parallel to the line \( P Q \), intersect the side \( Q T \) at points \( L \) and \( M \) respectively, and \( Q L = L M = M T \). Find the radius of the circle \( \Omega \) and the area of the triangle \( P Q T \), given that \( A B = 2 \sqrt{14} \), \( C D = 2 \sqrt{11} \), and the center \( O \) of the circle \( \Omega \) is located between the lines \( A B \) and \( C D \).

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