
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 $f(x) = 4\sin(2x + \frac{π}{3})$, where $x \in R$, the following propositions are given:

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

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

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

$④$ The graph of the function $y = f(x)$ is symmetrical about the line $x = -\frac{π}{6}$.

Identify the correct proposition(s).

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