
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 propositions, the correct ones are __________. (Fill in the serial numbers of all correct propositions)  
① A particle moves along a straight line with velocity $v=3t^2-2t-1$ (m/s), from the moment $t=0$ (s) to $t=3$ (s), the distance traveled by the particle is 15 (m);  
② If $x\in(0,\pi)$, then $\sin x < x$;  
③ If $f'(x_0)=0$, then the function $y=f(x)$ has an extremum at $x=x_0$;  
④ Given the function $f(x)= \sqrt{-x^{2}+4x}$, then $\int_{0}^{2} f(x)dx=\pi$.

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