
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 $f(x)=3\sin(2x-\frac{\pi}{3})$ with its graph denoted as $C$, determine the correct conclusion(s) from the following options (write out the numbers of all correct conclusions).
$①$ The graph $C$ is symmetrical about the line $x=\frac{11\pi}{12}$;
$②$ The graph $C$ is symmetrical about the point $(\frac{2\pi}{3}, 0)$;
$③$ The function $f(x)$ is decreasing in the interval $(-\frac{\pi}{12}, \frac{5\pi}{12})$;
$④$ By compressing the abscissa of the graph of the function $y=3\sin(x-\frac{\pi}{6})$ to half of its original value (without changing the ordinate), we can obtain graph $C$.

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