
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 functions $f(x)=3\sin (2x+ \frac {\pi}{6})$ and $g(x)=\tan (x+ \frac {\pi}{6})$, consider the following statements:  
① The graph of $f(x)$ is symmetric about the line $x=- \frac {\pi}{12}$;  
② The graph of $g(x)$ is centrally symmetric about $( \frac {\pi}{3},0)$;  
③ The function $g(x)$ is monotonically increasing within its domain;  
④ If the graph of $f(x)$ is translated to the left by $ \frac {\pi}{6}$ units, it becomes the graph of the function $y=3\cos 2x$;  
⑤ Given $f(x_{1})=f(x_{2})=0$, it follows that $x_{1}-x_{2}$ must be an integer multiple of $ \frac {\pi}{2}$.  
The correct statements are \_\_\_\_\_\_.

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