
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
Consider the function $f\left(x\right)=4\sin \left(2x+\frac{π}{3}\right)\left(x\in R\right)$. Among the following statements, the correct one(s) is/are:

$\left(①\right)$ The expression of $y=f\left(x\right)$ can be rewritten as $y=4\cos \left(2x-\frac{π}{6}\right)$;

$\left(②\right)$ $y=f\left(x\right)$ is a periodic function with the smallest positive period of $2π$;

$\left(③\right)$ The graph of $y=f\left(x\right)$ is symmetric about the point $\left(-\frac{π}{6},0\right)$;

$\left(④\right)$ The graph of $y=f\left(x\right)$ is symmetric about the line $x=\frac{5π}{6}$.

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