
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 rectangle and a regular hexagon are designed such that the area of the rectangle is numerically equal to twice its perimeter, and the area of the hexagon is numerically equal to three times its perimeter. If the length of the rectangle is twice its width, compare the apothem of the rectangle (which is half its width) with the apothem of the hexagon.
A) $\frac{1}{3}\text{ times the second}$
B) $\frac{1}{2}\text{ times the second}$
C) $1\text{ time the second}$
D) $2\text{ times the second}$
E) $3\text{ times the second}$

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