
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 concentric circles have diameters of 2 inches and 4 inches respectively. The smaller circle contains a square of side 1 inch, centered at the same center, with the rest of the area painted red. The area between the smaller circle and the larger circle is painted blue. Calculate the ratio of the blue-painted area to the red-painted area.

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