
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
For \( x, y, z \in (0,1] \), find the maximum value of the expression

$$
A = \frac{\sqrt{8 x^{4} + y} + \sqrt{8 y^{4} + z} + \sqrt{8 z^{4} + x} - 3}{x + y + z}
$$

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