
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 the three roots of the equation \(8 x^{3}+2012 x+2013=0\). Find the value of \((\alpha+\beta)^{3}+(\beta+\gamma)^{3}+(\gamma+\alpha)^{3}\).

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