
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
Suppose \( n \) is a natural number. For any real numbers \( x, y, z \), the inequality \(\left(x^{2} + y^{2} + z^{2}\right) \leqslant n \left(x^{4} + y^{4} + z^{4}\right)\) always holds. Then the minimum value of \( n \) is \(\qquad\)

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