
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 $n$. What is the value of $r$ in terms of $n$?
A) $\frac{n(\sqrt{3} - 1)}{2}$
B) $\frac{n(\sqrt{3} + 1)}{2}$
C) $n(\sqrt{3} - 1)$
D) $n(\sqrt{3} + 1)$

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