
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 called super cool if the number of square units in its area equals three times the number of units in its perimeter. This rectangle must also have integer side lengths. What is the sum of all different possible areas of super cool rectangles?

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