
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
Two circles have centers that are \( d \) units apart, and each has a diameter \( \sqrt{d} \). For any \( d \), let \( A(d) \) be the area of the smallest circle that contains both of these circles. Find \( \lim _{d \rightarrow \infty} \frac{A(d)}{d^{2}} \).

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