
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
Regarding the function $f(x) = 4\sin(2x + \frac{\pi}{3})$ ($x \in \mathbb{R}$), the following statements are made:
① The graph of $y=f(x)$, after being shifted to the right by $\frac{\pi}{3}$ units, is symmetric about the origin;
② The function $y=f(x)$ is a periodic function with a minimum positive period of $2\pi$;
③ The graph of $y=f(x)$ is symmetric about the point $(-\frac{\pi}{6}, 0)$;
④ The graph of $y=f(x)$ is symmetric about the line $x= \frac{\pi}{6}$.
Among these, the correct ones are __________. (Fill in all the numbers you think are correct)

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