
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 \(5^{\frac{1}{3}}, 5^{\frac{2}{3}}, 5^{\frac{3}{3}}, 5^{\frac{4}{3}}, \dots, 5^{\frac{n}{3}}\), determine the least positive integer \(n\) such that the product of the first \(n\) terms exceeds 1,000,000.
A) 6
B) 7
C) 8
D) 9
E) 10

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