
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
Given the progression \(8^{\frac{2}{11}}, 8^{\frac{3}{11}}, 8^{\frac{4}{11}}, \dots, 8^{\frac{(n+1)}{11}}\), calculate the least positive integer \(n\) such that the product of the first \(n\) terms of the progression exceeds 1,000,000.

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