
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 if the number of square units in its area equals thrice the number of units in its perimeter. This type of rectangle also must have integer side lengths. Find the sum of all possible different areas of such super rectangles.

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