
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 right triangle with integer leg lengths is termed "amazing" if the number of square units in its area equals three times the number of units in the sum of the lengths of its legs. Determine all possible areas of such "amazing" right triangles.

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