
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
Let \(ABCD\) be a rectangle with \(AB = 10\). Draw circles \(C_1\) and \(C_2\) with diameters \(AB\) and \(CD\) respectively. Let \(P\) and \(Q\) be the intersection points of \(C_1\) and \(C_2\). If the circle with diameter \(PQ\) is tangent to \(AB\) and \(CD\), then what is the area of the shaded region?

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