
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
Let real numbers $x$, $y$, $z$ satisfy $x+y+z=0$, and $(x-y)^2+(y-z)^2+(z-x)^2 \leq 2$. Find the maximum and minimum values of $x$.

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