
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 "smart" if the number of square units in its area is equal to three times the number of units in its perimeter. This rectangle must also have integer side lengths. What is the sum of all the different possible areas of smart rectangles?

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