
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
It is known that the roots of the equation $x^{5}+3 x^{4}-4044118 x^{3}-12132362 x^{2}-12132363 x-2011^{2}=0$ are all integers. How many distinct roots does the equation have?

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