
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
For the function $f(x)=4\sin\left(2x+\frac{\pi}{3}\right)$, where $x\in\mathbb{R}$, the following conclusions are made:<br/>① The graph of $y=f\left(x\right)$ is symmetric about the point $(-\frac{\pi}{6},0)$;<br/>② The graph of $y=f\left(x\right)$ is symmetric about the line $x=-\frac{\pi}{6}$;<br/>③ The expression of $y=f\left(x\right)$ can be written as $y=4\cos\left(2x-\frac{\pi}{6}\right)$;<br/>④ If $f(x_{1})=f(x_{2})=0$, then $x_{1}-x_{2}$ must be a multiple of $\pi$. Determine the correct conclusions.

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