
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 circle of radius $2m$ is inscribed in an equilateral triangle. Then a square is inscribed in that circle, and a new circle is inscribed in this latter square. If $S_n$ is the sum of the areas of the first $n$ circles so inscribed, then, as $n$ grows beyond all bounds, what does $S_n$ approach?
A) $4\pi m^2$
B) $8\pi m^2$
C) $12\pi m^2$
D) $16\pi m^2$

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