
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 defined as excellent if the number of square units in its area is three times the number of units in its perimeter. The rectangle must also have integer side lengths. What is the sum of all the different possible areas of excellent rectangles?

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