
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 is inscribed in a square of side $m = 2$. Then a square is inscribed in that circle, then a circle is inscribed in that latter square, and so on. If $S_n$ is the sum of the areas of the first $n$ circles so inscribed, find the limit of $S_n$ as $n$ grows beyond all bounds.
A) $\frac{\pi}{4}$
B) $\pi$
C) $2\pi$
D) $4\pi$
E) $\frac{3\pi}{2}$

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