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

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