
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 $\eta_1, \eta_2,$ and $\eta_3$ be complex numbers such that:
\[\eta_1 + \eta_2 + \eta_3 = 2\]
\[\eta_1^2 + \eta_2^2 + \eta_3^2 = 5\]
\[\eta_1^3 + \eta_2^3 + \eta_3^3 = 10\]
Compute $\eta_1^5 + \eta_2^5 + \eta_3^5$.

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