
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 $f(x) = \sin(2x + \frac{\pi}{6})$, 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 $(\frac{5\pi}{12}, 0)$.  
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 $y = \sin(x + \frac{\pi}{6})$ to half of their original values (keeping the y-coordinates unchanged).  
Among these statements, the correct ones are \_\_\_\_\_\_.

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