
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
Find all triples of real numbers \( x, y, z \) such that \( 1 + x^4 \leq 2(y - z)^2 \), \( 1 + y^4 \leq 2(z - x)^2 \), and \( 1 + z^4 \leq 2(x - y)^2 \).

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