
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
A $4$-inch and $20$-inch diameter poles are placed side by side and bound together by a wire. Find the length of the shortest wire that will perfectly enclose both poles.
A) \( 8\sqrt{5} + 14\pi \)
B) \( 8\sqrt{5} + 15\pi \)
C) \( 8\sqrt{5} + 14\frac{1}{3}\pi \)
D) \( 10\sqrt{5} + 14\pi \)
E) \( 12\sqrt{5} + 14\frac{1}{3}\pi \)

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