
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 $f(x)=\sin 2x- \sqrt{3}(\cos^2x-\sin^2x)$ is denoted as $C$. Among the following conclusions, the correct one(s) is(are) __.

$(1)$ The graph $C$ is symmetric about the line $x= \frac{11}{12}\pi$;

$(2)$ The graph $C$ is symmetric about the point $(\frac{2\pi}{3},0)$;

$(3)$ The graph of the function $f(x)$ in the interval $6$ can be obtained by shifting the graph $C$ to the right by $\frac{\pi}{3}$ units.

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