
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
Let $\alpha_1, \alpha_2,$ and $\alpha_3$ be complex numbers such that:
\[\alpha_1+\alpha_2+\alpha_3=2,\]
\[\alpha_1^2+\alpha_2^2+\alpha_3^2=6,\]
\[\alpha_1^3+\alpha_2^3+\alpha_3^3=14.\]
Compute $\alpha_1^{7} + \alpha_2^{7} + \alpha_3^{7}$.

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