
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 $f(x)=3\sin (2x+ \frac {\pi}{6})$, the following statements are given:  
$(1)$ The graph is centrally symmetric about the origin;      $(2)$ The graph is symmetric about the line $x= \frac {\pi}{6}$;  
$(3)$ The maximum value of the function $f(x)$ is $3$;      $(4)$ The function is monotonically increasing in the interval $\left[- \frac {\pi}{4}, \frac {\pi}{4}\right]$.  
Among these, the correct statement numbers are \_\_\_\_\_\_ .

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