
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 polynomial \(p(x) = x^n + nx^{n-1} + a_2 x^{n-2} + \cdots + a_n\). Let \(v_i (1 \leq i \leq n)\) be all the roots of \(p(x)\), and given that \(\left|\gamma_1\right|^{16} + \left|\gamma_2\right|^{16} + \cdots + \left|\gamma_n\right|^{16} = n\), find the roots of \(p(x)\).

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