
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
Determine all possible values of $m$, where $m$ is the exact number of integer roots, counting multiplicity, of the polynomial:
\[x^5 + px^4 + qx^3 + rx^2 + sx + t = 0\]
given that all coefficients are integers.

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