
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 $f(x) = 3\sin(2x + \frac{\pi}{6})$, consider the following statements:  
① The graph is 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 $[-\frac{\pi}{4}, \frac{\pi}{4}]$.  
Among these, the correct statement(s) is/are __________.

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