
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 \(C\) with radius 6 has diameter \(\overline{AB}\). Circle \(D\) is internally tangent to circle \(C\) at \(A\). Circle \(E\) is internally tangent to circle \(C\), externally tangent to circle \(D\), and tangent to \(\overline{AB}\). The radius of circle \(D\) is four times the radius of circle \(E\), and can be written in the form \(\sqrt{p}-q\), where \(p\) and \(q\) are positive integers. Find \(p+q\).

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