
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
Circles of diameter $2$ inches and $6$ inches have the same center. The smaller circle is painted yellow, and the portion outside the smaller circle and inside the larger circle is painted green. Determine the ratio of the green-painted area to the yellow-painted area.

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