
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 \( r \) is given. A square is inscribed in this circle, then a circle is inscribed in that square, and so on. If \( T_n \) is the sum of the areas of the first \( n \) circles so inscribed, then, as \( n \) grows beyond all bounds, \( T_n \) approaches:
- **Note**: No choices provided yet.
A) \( \pi r^2 \)
B) \( \frac{\pi r^2}{2} \)
C) \( 2\pi r^2 \)
D) \( \frac{3\pi r^2}{2} \)
E) \( 4\pi r^2 \)

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