
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 $f(x) = 4\sin(2x + \frac{\pi}{3})$, $(x \in \mathbb{R})$, determine the correct proposition(s) from the following:

1. $y = f(x)$ is a periodic function with the smallest positive period of $2\pi$;
2. The graph of $y = f(x)$ is symmetrical about the point $(-\frac{\pi}{6}, 0)$;
3. The graph of $y = f(x)$ is symmetrical about the line $x = -\frac{5\pi}{12}$.

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