
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 For all $x \in (0, +\infty)$, $x^2 > x^3$;  
② There exists an $x \in (0, +\infty)$, such that $x > e^x$;  
③ The function $f(x)$ is defined on $\mathbb{R}$, and $f(2-x) = f(x)$, then the graph of $f(x)$ is symmetric about the line $x=1$;  
④ If the function $f(x) = \log(x^2 + ax - a)$ has its range as $\mathbb{R}$, then $a \leq -4$ or $a \geq 0$;  
Among these propositions, the correct ones are     . (Write down the numbers of all correct propositions)

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