
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 rectangle, and then a rectangle is inscribed in this circle. Finally, a circle is inscribed in this second rectangle. If the ratio of the length to the width of the first rectangle is 3:2, what is the ratio of the area of the smaller circle to the area of the original rectangle?

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