
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
Let $p, q,$ and $r$ be distinct prime numbers, where $1$ is not considered a prime. What is the smallest positive perfect cube that has $n = pq^3r^4$ as a divisor?
A) $p^6q^6r^6$
B) $(pq^3r^2)^3$
C) $(pqr^2)^3$
D) $(p^2q^3r^3)^3$
E) $4p^3q^3r^4$

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