
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
Divide the natural numbers 1, 2, 3, ..., 99 into three groups. If the average number of each group is exactly equal, then the product of these three average numbers is ____.

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