
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 $f(x)=\sin \left(2x+ \frac {\pi}{6}\right)$, consider the following statements:  
$(1)$ The graph of the function is symmetric about the line $x=- \frac {\pi}{12}$;      
$(2)$ The graph of the function is symmetric about the point $\left( \frac {5\pi}{12},0\right)$;  
$(3)$ The graph of the function can be obtained by shifting the graph of $y=\sin 2x$ to the left by $\frac {\pi}{6}$ units;  
$(4)$ The graph of the function can be obtained by compressing the $x$-coordinates of the graph of $y=\sin \left(x+ \frac {\pi}{6}\right)$ to half of their original values (the $y$-coordinates remain unchanged);  
Among these statements, the correct ones are \_\_\_\_\_\_.

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