
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 real numbers $A, B, C$ such that for any real numbers $x, y, z$, the following inequality holds:
$$
A(x-y)(x-z)+B(y-z)(y-x)+C(z-x)(z-y) \geq 0
$$

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