
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
Consider two circles, where the diameter of the first circle increases by $2\pi$ units and this increase leads to a proportional increase in the circumference of the second circle by $P$ units. Calculate $P$.
A) $\pi$
B) $\pi^2$
C) $2\pi$
D) $2\pi^2$
E) $4\pi^2$

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