
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 the diagram below, circles \( C_{1} \) and \( C_{2} \) have centers \( O_{1} \) and \( O_{2} \), respectively. The radii of the circles are \( r_{1} \) and \( r_{2} \), with \( r_{1} = 3r_{2} \). Circle \( C_{2} \) is internally tangent to \( C_{1} \) at point \( P \). Chord \( XY \) of \( C_{1} \) has length 20, is tangent to \( C_{2} \) at point \( Q \), and is parallel to the line segment \( O_{2}O_{1} \). Determine the area of the shaded region, which is the region inside \( C_{1} \) but not \( C_{2} \).

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