
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
For the function $f(x)$ defined on $\mathbb{R}$, three statements are given:  
① If $f(-2) = f(2)$, then $f(x)$ is an even function;  
② If $f(-2) \neq f(2)$, then $f(x)$ is not an even function;  
③ If $f(-2) = f(2)$, then $f(x)$ is definitely not an odd function.  
Among these, the correct statement number is.

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