
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 termed "great" if the number of square units in its area equals three times the number of units in its perimeter, and it has integer side lengths. Calculate the sum of all different possible areas of such great rectangles.

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