
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
Consider the function $y = f(x) = 4\sin\left(2x + \frac{\pi}{3}\right)$, where $x$ is in the set of real numbers $ \mathbb{R}$. The following propositions about the function are given:
1. The expression for $y = f(x)$ can be rewritten as $y = 4\cos\left(2x - \frac{\pi}{6}\right)$.
2. The function $y = f(x)$ is a periodic function with the smallest positive period of $2\pi$.
3. The graph of the function $y = f(x)$ is symmetric about the point $\left(-\frac{\pi}{6}, 0\right)$.
4. The graph of the function $y = f(x)$ is symmetric about the line $x = -\frac{\pi}{6}$.

Identify the correct propositions.

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