
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
An acute triangle  $ABC$  has side lenghths  $a$ ,  $b$ ,  $c$  such that  $a$ ,  $b$ ,  $c$  forms an arithmetic sequence. Given that the area of triangle  $ABC$  is an integer, what is the smallest value of its perimeter?

*2017 CCA Math Bonanza Lightning Round #3.3*

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