
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 triangle with integral sides has a perimeter of 12. Calculate the area of the triangle when the sides of the triangle are equal to the three smallest integral values that satisfy the triangle inequality.

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