
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
Determine the correct proposition numbers from the following five propositions.

(1) The minimum positive period of the function $y = \left|\sin x + \frac{1}{2}\right|$ is $T = 2\pi$;

(2) The graph of the function $f(x) = 4\cos\left(2x - \frac{\pi}{6}\right)$ is symmetric about the point $\left(-\frac{\pi}{6}, 0\right)$;

(3) The graph of the function $y = \sin\left(2x + \frac{\pi}{3}\right)$ is symmetric about the line $x = \frac{\pi}{3}$;

(4) In the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, the equation $\tan x = \sin x$ has 3 solutions;

(5) In $\triangle ABC$, if $A > B$, then $\sin A > \sin B$.

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