
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 the real numbers \( x, y, z \in (0, \sqrt{5}) \) satisfy \( x^{4} + y^{4} + z^{4} \geqslant 27 \), find the maximum value of \( \frac{x}{x^{2} - 5} + \frac{y}{y^{2} - 5} + \frac{z}{z^{2} - 5} \).

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