
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
For the function $f(x)= \begin{cases}\sin \pi x, & x\in[0,2] \\ \frac {1}{2}f(x-2), & x\in(2,+\infty)\end{cases}$, there are the following 4 propositions:  
1. For any $x_{1}, x_{2}\in[0,+\infty)$, $|f(x_{1})-f(x_{2})|\leqslant 2$ always holds;  
2. $f(x)=2^{k}f(x+2k) (k\in\mathbb{N}^{*})$ holds for all $x\in[0,+\infty)$;  
3. For any $x > 0$, the inequality $f(x)\leqslant \frac {k}{x}$ always holds, then the range of the real number $k$ is $[\frac {9}{8},+\infty)$;  
4. The function $y=f(x)-\ln (x-1)$ has 3 zeros;  
Then, the sequence numbers of all true propositions are ______.

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