
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 $f(x)=\sin(\frac{1}{2}x+\frac{π}{3})$, the correct statement among the following four is ____.<br/>① The graph of the function $f(x)$ is symmetric about the line $x=\frac{2π}{3}$;<br/>② The function $f(x)$ is monotonically increasing on $[-\frac{π}{3},\frac{π}{2}]$;<br/>③ The graph of the function $f(x)$ is symmetric about the point $(-\frac{2π}{3},0)$;<br/>④ The range of the function $f(x)$ on $[-\frac{4π}{3},π]$ is $[-\frac{\sqrt{3}}{2},\frac{1}{2}]$.

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