
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 propositions given below, the serial numbers of all correct propositions are __________.

1. If $\vec{a} \cdot \vec{b} > 0$, then the angle between $\vec{a}$ and $\vec{b}$ is acute;

2. For all $x,y \in \mathbb{R}$, if $x+y \neq 0$, then $x \neq 1$ or $y \neq -1$;

3. If real numbers $x,y$ satisfy $x^2+y^2=1$, then the maximum value of $\frac{y}{x+2}$ is $\frac{\sqrt{3}}{3}$;

4. The graph of the function $f(x)=3\sin\left(2x-\frac{\pi}{3}\right)$ is symmetric about the point $\left(\frac{2\pi}{3},0\right)$.

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