
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 graph of the function $f(x)=\sin 2x- \sqrt {3}(\cos ^{2}x-\sin ^{2}x)$ is denoted as $C$. Among the following conclusions, the correct one(s) is(are) ______.  
$(1)$ The graph $C$ is symmetric about the line $x= \dfrac {11}{12}\pi$;  
$(2)$ The graph $C$ is symmetric about the point $( \dfrac {2\pi}{3},0)$;  
$(3)$ The function $f(x)$ is increasing in the interval $(- \dfrac {\pi}{12}, \dfrac {5\pi}{12})$;  
$(4)$ The graph of $y=2\sin 2x$ can be obtained by shifting the graph $C$ to the right by $\dfrac {\pi}{3}$ units.

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