
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 $f(x) = \sin \left(2x+ \frac{\pi}{6}\right)$, then the following statements:

(1) The graph of $f(x)$ is symmetric about the line $x= \frac{\pi}{3}$;

(2) The graph of $f(x)$ is symmetric about the point $\left( \frac{\pi}{6},0\right)$;

(3) The smallest positive period of $f(x)$ is $\pi$, and it is an increasing function on the interval $\left[0, \frac{\pi}{12}\right]$;

(4) Shifting the graph of $f(x)$ to the right by $\frac{\pi}{12}$ units results in the graph of an odd function.

Among these, the correct statements are               _．_

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