
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
The area of a square equals the square of the length of one of its sides. The perimeter is four times the side length. If the sum of the areas of two squares is 85 and the difference of their areas is 41, what is the sum of their perimeters?

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