
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
$\zeta_1, \zeta_2,$ and $\zeta_3$ are complex numbers such that
\[\zeta_1+\zeta_2+\zeta_3=2\]
\[\zeta_1^2+\zeta_2^2+\zeta_3^2=5\]
\[\zeta_1^3+\zeta_2^3+\zeta_3^3=14\]
Compute $\zeta_1^{7} + \zeta_2^{7} + \zeta_3^{7}$.

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