
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
Regions I, II, III, and IV are bounded by squares. The perimeter of region I is 16 units, the perimeter of region II is 20 units, and the perimeter of region IV is 32 units. What is the ratio of the area of region III to the area of region IV? Assume that the side of region III is three times the side of region I.

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