
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
A rectangle is considered special if the number of square units in its area is equal to three times the number of units in its perimeter. The rectangle must have integer side lengths. Determine the sum of all the different possible areas of such special rectangles.

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