
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
The area of a circle is tripled when its radius \( r \) is increased by \( n \). Find \( r \) in terms of \( n \).
A) \( \frac{n(\sqrt{3} + 1)}{2} \)
B) \( \frac{n(\sqrt{3} - 1)}{2} \)
C) \( n\sqrt{3} \)
D) \( \frac{n}{\sqrt{3} - 1} \)

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