
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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