
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 statements are given:  
$(1)$ The smallest positive period of the function $y=f(x)$ is $\pi$.  
$(2)$ The initial phase of the function $y=f(x)$ is $2x+ \frac {\pi}{3}$.  
$(3)$ The amplitude of the function $y=f(x)$ is $4$.  
Among these, the correct ones are \_\_\_\_\_\_.

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