
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
If a function $f(x, y, z)$ satisfies $f(a, b, c) = f(b, c, a) = f(c, a, b)$, then the function $f(x, y, z)$ is called a cyclically symmetric function. For example, $f(a, b, c) = abc$ is a cyclically symmetric function. Which of the following statements is correct?

① The function $f(x, y, z) = x^2 - y^2 + z$ is not a cyclically symmetric function.  
② The function $f(x, y, z) = x^2(y-z) + y^2(z-x) + z^2(x-y)$ is a cyclically symmetric function.  
③ If the functions $f(x, y, z)$ and $g(x, y, z)$ are both cyclically symmetric functions, then the function $f(x, y, z) - g(x, y, z)$ is also a cyclically symmetric function.  
④ If $A, B, C$ are the three interior angles of $\triangle ABC$, then $f(A, B, C) = 2 + \cos C \cdot \cos(A-B) - \cos^2 C$ is a cyclically symmetric function.

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