
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
Given the function $f(x) = \sin x + \sqrt{3}\cos x$, which of the following statements are correct? (Fill in the numbers of all correct statements.)

① The maximum value of the function $f(x)$ is 2;  
② The graph of the function $f(x)$ is symmetric about the point $\left(-\frac{\pi}{6}, 0\right)$;  
③ The graph of the function $f(x)$ is symmetric about the x-axis with the graph of the function $h(x) = 2\sin\left(x - \frac{2\pi}{3}\right)$;  
④ If a real number $m$ makes the equation $f(x) = m$ have exactly three real solutions $x_1$, $x_2$, $x_3$ in the interval $[0, 2\pi]$, then $x_1 + x_2 + x_3 = \frac{7\pi}{3}$.

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