
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]


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The graph of the function $f(x)=3\sin (2x- \frac{\pi}{3})$ is denoted as _C_. Among the following conclusions, the correct one(s) is/are _____________

- $①$ The graph _C_ is symmetric about the line $x= \frac{11\pi}{12}$;
- $②$ The graph _C_ is symmetric about the point $(\frac{2\pi}{3},0)$;
- $③$ The function $f(x)$ is increasing in the interval $(- \frac{\pi}{12}, \frac{5\pi}{12})$;
- $④$ The period of the function $f(x)=3|\sin (2x-\frac{\pi}{3})|$ is $\frac{\pi}{2}$.

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