
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 A, B, and C are bounded by squares. The perimeter of region A is 16 units, the perimeter of region B is 40 units, and the perimeter of region C is three times the perimeter of region B. What is the ratio of the area of region A to the area of region C? Express your answer as a common fraction.

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