
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
Tom has an equilateral triangle with a side length of 12 inches. He wants to cut it into six pieces that have equal areas. To the nearest hundredth of an inch, what is the number of inches in the greatest perimeter among the six pieces?

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