
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 circular playground is designed to be enlarged to create two different new circular playgrounds. The first new playground's diameter is three times that of the original playground's diameter, and the second new playground's diameter is four times that of the original playground's diameter. What is the ratio of the areas of the first new playground to the second new playground?

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