
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 a triangle whose side lengths are integers and the product of the side lengths is equal to 600. Additionally, the perimeter of the triangle should be the smallest possible. Solve the same problem if the product is 144.

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