
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 $\alpha, \beta,$ and $\gamma$ be complex numbers such that:
\[\alpha + \beta + \gamma = 2,\]
\[\alpha^2 + \beta^2 + \gamma^2 = 5,\]
\[\alpha^3 + \beta^3 + \gamma^3 = 10.\]
Compute $\alpha^7 + \beta^7 + \gamma^7$.

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