
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
Given that
$$
\begin{aligned}
\alpha+\beta+\gamma & =14 \\
\alpha^{2}+\beta^{2}+\gamma^{2} & =84 \\
\alpha^{3}+\beta^{3}+\gamma^{3} & =584
\end{aligned}
$$
find $\max \{\alpha, \beta, \gamma\}$.


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