
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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Consider the function $f(x)=2\sin \left(2x-\frac{\pi }{6}\right)\left(x\in \mathbb{R}\right)$. Among the following statements:

(1) If $f(x\_1)=f(x\_2)=0$, then $x\_1-x\_2$ is an integer multiple of $\pi$;

(2) The expression can be rewritten as $f(x)=2\cos \left(2x-\frac{2\pi }{3}\right)$;

(3) The graph of the function is symmetric with respect to the point $\left(\frac{\pi }{3},0\right)$;

(4) The graph of the function is symmetric with respect to the line $x=-\frac{\pi }{6}$;

Determine the correct statement number(s).

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