
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 $12^{\dfrac{1}{13}}, 12^{\dfrac{2}{13}}, 12^{\dfrac{3}{13}}, \dots, 12^{\dfrac{n}{13}}$. 
Find the smallest positive integer $n$ such that the product of the first $n$ terms of this progression exceeds $1,000,000$.
A) 11
B) 12
C) 13
D) 14
E) 15

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