
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 a circle \(\omega\) centered at \(O\), \(AA'\) and \(BB'\) are diameters perpendicular to each other such that the points \(A, B, A', B'\) are arranged in an anticlockwise direction in this order. Let \(P\) be a point on the minor arc \(A'B'\) such that \(AP\) intersects \(BB'\) at \(D\) and \(BP\) intersects \(AA'\) at \(C\). Suppose the area of the quadrilateral \(ABCD\) is 100. Find the radius of \(\omega\).

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