
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
Among the following statements:

① If $f(x) = ax^2 + (2a+b)x + 2$ (where $x \in [2a－1, a+4]$) is an even function, then the real number $b = 2$;  
② $f(x)$ represents the smaller one between $-2x + 2$ and $-2x^2 + 4x + 2$, then the maximum value of $f(x)$ is 1;  
③ If the increasing interval of the function $f(x) = |2x + a|$ is $[3, +\infty)$, then $a = -6$;  
④ Given that $f(x)$ is a function defined on $\mathbb{R}$, not constantly zero, and for any $x, y \in \mathbb{R}$, it satisfies $f(x \cdot y) = x \cdot f(y) + y \cdot f(x)$, then $f(x)$ is an odd function.  
Among these, the correct statement(s) is (are)        (Note: Fill in all the numbers you think are correct).

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