
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 $a, b,$ and $c$ be distinct prime numbers. Determine the smallest positive perfect cube for which $n = a^2b^3c^5$ is a divisor.
A) \( a^3b^6c^6 \)
B) \( a^2b^3c^5 \)
C) \( (abc^2)^3 \)
D) \( (ab^2c^3)^3 \)
E) \( a^6b^6c^6 \)

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