
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 a third-degree polynomial with the leading coefficient 1, given that its three roots \(x_{1}, x_{2}, x_{3}\) satisfy the equations: \(\alpha = x_{1} + x_{2}\), \(\beta = x_{1} + x_{3}\), \(\gamma = x_{2} + x_{3}\), where \(\alpha, \beta, \gamma\) are the roots of the polynomial \(x^{3} - 12x^{2} + 44x - 46\).

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