
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
Regarding the function $f(x) = 4\sin(2x - \frac{\pi}{3})$ ($x \in \mathbb{R}$), the following statements are made:
(1) $y = f(x + \frac{4\pi}{3})$ is an even function;
(2) To obtain the graph of the function $g(x) = -4\sin(2x)$, one only needs to shift the graph of $f(x)$ to the right by $\frac{\pi}{3}$ units;
(3) The graph of $y = f(x)$ is symmetric about the line $x = -\frac{\pi}{12}$;
(4) The increasing intervals of $y = f(x)$ in $[0, 2\pi]$ are $[0, \frac{5\pi}{12}]$ and $[\frac{11\pi}{12}, 2\pi]$;
(5) The period of $y = f(x)$ is $\pi$. The correct statement numbers are __________.

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