
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
Find all integer side length pairs of a right triangle such that the number of square units in its area is equal to three times the sum of its leg lengths. Calculate the sum of all distinct areas from these triangles.

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