
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, and III are bounded by shapes. The perimeter of region I is 16 units and the perimeter of region II is 36 units. Region III is a triangle with a perimeter equal to the average of the perimeters of regions I and II. What is the ratio of the area of region I to the area of region III? Express your answer as a common fraction.

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