
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
Find integers \( m \) and \( n \) such that \( n^2 \) is a multiple of \( m \), \( m^3 \) is a multiple of \( n^2 \), \( n^4 \) is a multiple of \( m^3 \), \( m^5 \) is a multiple of \( n^4 \), but \( n^6 \) is not a multiple of \( m^5 \).

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