
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 square is inscribed in a circle of radius $r$, then a circle is inscribed in that square, then a square is inscribed in the latter circle, and so on. What is the limit of the sum of the areas of the first $n$ squares as $n$ grows beyond all bounds, where $r$ is the radius of the initial circle?
A) $2r^2$
B) $3r^2$
C) $4r^2$
D) $5r^2$
E) $6r^2$

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