
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
When the radius $r$ of a circle is increased by $5$, the area is quadrupled. What was the original radius $r$? Additionally, find the new perimeter of the circle after this radius increase.
A) Original radius: 4, New perimeter: $18\pi$
B) Original radius: 5, New perimeter: $20\pi$
C) Original radius: 6, New perimeter: $22\pi$
D) Original radius: 5, New perimeter: $19\pi$

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