
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
The function $f(x)=3\sin (2x- \frac {\pi }{3})$ has a graph denoted as $C$. Among the following conclusions, the correct one(s) is/are _______ (write out the number(s) of all correct conclusions)
$(1)$ The graph $C$ is symmetric about the line $x= \frac {11}{12}\pi $;
$(2)$ 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 graph $C$ can be obtained by shifting the graph of $y=3\sin 2x$ to the right by $\frac {\pi }{3}$ units.

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