
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
Consider the following propositions:
1. The correlation coefficient $r$ between variables $y$ and $x$ is $-0.9568$, and the critical value for the correlation coefficient is $r_{0.05}=0.8016$. Hence, there is a linear relationship between $y$ and $x$.
2. If $a>0$ and $b>0$, then the inequality $a^3+b^3\geq 3ab^2$ always holds.
3. For the function $f(x)=2x^2+mx+n$, if $f(a)>0$ and $f(b)>0$, then the function has at most one zero in the interval $(a, b)$.
4. The graphs of $y=f(x-2)$ and $y=f(2-x)$ are symmetrical about $x=2$.

The sequence numbers of all correct propositions are ____.

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