
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
In Squareland, only squares live. Except for two exceptions, each of them has two friends, one whose perimeter is \(8 \text{ cm}\) less and the other whose perimeter is \(8 \text{ cm}\) more. The average side length of a Squareland square is \(15 \text{ cm}\). No two squares are identical, and the perimeter of the smallest square is equal to the side length of the largest square. Determine:

a) The number of inhabitants in Squareland,

b) The dimensions of the largest and smallest Squareland square,

c) The average area of a "Squarelandian".

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