
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, then a square is inscribed in this circle, and finally, a circle is inscribed in this square. However, the side length of the smaller square inscribed in the first circle is \(3r\) instead of \(2r\) where \(r\) is the radius of the smaller circle. What is the ratio of the area of the smaller circle to the area of the larger square?

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