
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 is called a Pythagorean triangle if the lengths of all its sides are natural numbers. Find the largest integer that divides the product of the side lengths of any Pythagorean triangle.

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