
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
Consider the cubic polynomial \(x^3 + bx^2 + cx + d = 0\) where \(b\), \(c\), and \(d\) are integers. Determine all possible values of \(m\), where \(m\) is the exact number of distinct integer roots of the polynomial.

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