
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
Circle \( B \) has radius \( 6\sqrt{7} \). Circle \( A \), centered at point \( C \), has radius \( \sqrt{7} \) and is contained in \( B \). Let \( L \) be the locus of centers \( C \) such that there exists a point \( D \) on the boundary of \( B \) with the following property: if the tangents from \( D \) to circle \( A \) intersect circle \( B \) again at \( X \) and \( Y \), then \( XY \) is also tangent to \( A \). Find the area contained by the boundary of \( L \).

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