
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 \(x, y, z \in (0, 2]\), find the maximum value of the expression

\[ 
A = \frac{\left(x^{3} - 6\right) \sqrt[3]{x + 6} + \left(y^{3} - 6\right) \sqrt[3]{y + 6} + \left(z^{3} - 6\right) \sqrt[3]{z + 6}}{x^{2} + y^{2} + z^{2}}
\]

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