
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 $f(x)=\sqrt{2}\sin(4x+\frac{π}{6})$. Among the following four statements:<br/>① The graph of the function $f(x)$ is symmetric with respect to the point $(\frac{π}{3},0)$;<br/>② The function $f(x)$ has $8$ extreme points in the interval $(-\pi ,\pi )$;<br/>③ The maximum value of the function $f(x)$ in the interval $[-\frac{π}{8},\frac{π}{8}]$ is $\sqrt{2}$;<br/>④ The function $f(x)$ is monotonically increasing in the interval $(-\frac{π}{4},\frac{π}{4})$.<br/>The correct statements are ____.

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