
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
Does there exist a right-angled triangle whose sides are all integers, and its area is equal to its perimeter? If it exists, determine the lengths of its three sides. If it does not exist, explain why.

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