
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
Non-negative numbers \(x, y, z\) satisfy the inequalities \(5 \leq x, y, z \leq 8\).

What is the maximum and minimum value that the quantity \(S=2 x^{2} y^{2} + 2 x^{2} z^{2} + 2 y^{2} z^{2} - x^{4} - y^{4} - z^{4}\) can take?

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