
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
In a geometric sequence, the terms are given by $3^{\frac{1}{6}}, 3^{\frac{2}{6}}, 3^{\frac{3}{6}}, 3^{\frac{4}{6}},\dots , 3^{\frac{n}{6}}$. Determine the smallest positive integer \( n \) such that the product of the first \( n \) terms of the sequence exceeds \( 1,000 \).
A) 5
B) 6
C) 7
D) 8

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