
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 following propositions:

(1) The graph of the function $y=3^{x} (x \in \mathbb{R})$ is symmetric to the graph of the function $y=\log_{3}x (x > 0)$ with respect to the line $y=x$;

(2) The smallest positive period of the function $y=|\sin x|$ is $2\pi$;

(3) The graph of the function $y=\tan (2x+\frac{\pi}{3})$ is centrally symmetric about the point $\left(-\frac{\pi}{6},0\right)$;

(4) The monotonic decreasing interval of the function $y=2\sin \left(\frac{\pi}{3}-\frac{1}{2}x\right), x \in [-2\pi, 2\pi]$ is $\left[-\frac{\pi}{3},\frac{5\pi}{3}\right]$.

The correct proposition numbers are $\boxed{(1)(3)(4)}$.

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