
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 statements from the following four propositions:
1. The domain of the function $y = \tan\left(x + \frac{\pi}{4}\right)$ is $\left\{x \mid x \neq \frac{\pi}{4} + k\pi, k \in \mathbb{Z}\right\}$.
2. Given that $\sin\alpha = \frac{1}{2}$, and $\alpha \in [0, 2\pi]$, then the set of possible values for $\alpha$ is $\left\{\frac{\pi}{6}\right\}$.
3. If the graph of the function $f(x) = \sin 2x + a\cos 2x$ is symmetric about the line $x = -\frac{\pi}{8}$, then the value of $a$ is -1.
4. The function $y = \cos^2 x + \sin x$ has a minimum value of -1.

Fill in the blank with the correct proposition numbers: __________.

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