
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 that the function $f(x)$ is differentiable on $\mathbb{R}$, and the function $F(x) = f(x^2 - 4) + f(4 - x^2)$, consider the following four statements: (1) $F(0) = 0$ (2) $F'(±2) = 0$ (3) $F'(0) = 0$ (4) The graph of $F'(x)$ is symmetric about the origin. Among these, the correct statement(s) is/are.

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