
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
Given a regular hexagon $ABCDEF$ with side length $6$ feet. A circle passes through vertices $A$ and $E$ and is tangent to the extension of side $CD$. Find the radius, in feet, of the circle.
A) $9$
B) $6$
C) $7$
D) $8\sqrt{2}$
E) $9\sqrt{2}$

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