
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 the following four propositions:  
① If $f(-2) \neq f(2)$, then $f(x)$ is not an even function;  
② When $n \in \{0, 1\}$, the graph of the power function $y = x^n$ is a straight line;  
③ The contrapositive of the proposition "If $a \neq 0$ and $b \neq 0$, then $ab \neq 0$";  
④ The necessary and sufficient condition for the cubic function $f(x) = ax^3 + bx^2 + cx + d$ to have an extremum is $b^2 - 3ac \geq 0$.  
The correct propositions are numbered as follows.

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