
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:

1. The domain of the function $y=\tan \left( x+\frac{\pi }{4} \right)$ is $\left\{ x\mid x=\frac{\pi }{4}+k\pi ,k\in \mathbb{Z} \right\}$;

2. Given $\sin \alpha =\frac{1}{2}$, and $\alpha\in[0,2\pi]$, then the set of values for $\alpha$ is $\left\{ \frac{\pi }{6} \right\}$;

3. The smallest positive period of the function $y=\sin \left( 2x+\frac{\pi }{3} \right)+\sin \left( 2x-\frac{\pi }{3} \right)$ is $\pi$;

4. The minimum value of the function $y=\cos ^{2}x+\sin x$ is $-1$.

Fill in the correct proposition numbers on the line __________.

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