
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
Given the equation \(x^{4} + 5x^{3} + 6x^{2} + 5x + 1 = 0\) with roots \(x_{1}, x_{2}, x_{3}, x_{4}\) in the complex domain, find the value of \(x_{1}^{3} + x_{2}^{3} + x_{3}^{3} + x_{4}^{3} = \qquad \).

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