
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
Regarding the function $f(x)=4\sin (2x+ \frac {\pi}{3})$, $(x\in\mathbb{R})$, the following propositions are given:  
$(1)y=f(x)$ is a periodic function with a minimum positive period of $2\pi$;  
$(2)y=f(x)$ can be rewritten as $y=4\cos (2x- \frac {\pi}{6})$;  
$(3)y=f(x)$'s graph is symmetric about $(- \frac {\pi}{6},0)$;  
$(4)y=f(x)$'s graph is symmetric about the line $x=- \frac {\pi}{6}$;  
Among these, the true propositions are numbered \_\_\_\_\_\_.

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