
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
Among the following four propositions, the number(s) of the true proposition(s) is ______.

(1) The function $y=\sin(2x+\frac{\pi}{3})$ is monotonically increasing in the interval $(-\frac{\pi}{3},\frac{\pi}{6})$.

(2) The graph of the function $y=\cos(x+\frac{\pi}{3})$ is symmetric about the point $(\frac{\pi}{6},0)$.

(3) The graph of the function $y=\tan(x+\frac{\pi}{3})$ is symmetric about the line $x=\frac{\pi}{6}$.

(4) Translating the graph of the function $y=3\sin(2x+\frac{\pi}{3})$ to the right by $\frac{\pi}{6}$ results in the graph of the function $y=3\sin 2x$.

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