
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
Let the direction vectors of lines $a$ and $b$ be $\vec{e}_1$ and $\vec{e}_2$, respectively, and let the normal vector of plane $\alpha$ be $\vec{n}$. Consider the following reasoning:  
1. $$\begin{Bmatrix} \vec{e}_1 \parallel \vec{e}_2 \\ \vec{e}_1 \parallel \vec{n} \end{Bmatrix} \Rightarrow b \parallel \alpha$$  
2. $$\begin{Bmatrix} \vec{e}_1 \parallel \vec{n} \\ \vec{e}_2 \parallel \vec{n} \end{Bmatrix} \Rightarrow a \parallel b$$  
3. $$\begin{Bmatrix} \vec{e}_1 \parallel \vec{n} \\ b \not\subset \alpha \\ \vec{e}_1 \perp \vec{e}_2 \end{Bmatrix} \Rightarrow b \parallel \alpha$$  
4. $$\begin{Bmatrix} \vec{e}_1 \parallel \vec{e}_2 \\ \vec{e}_1 \parallel \vec{n} \end{Bmatrix} \Rightarrow b \perp \alpha$$  
The correct reasoning number(s) is/are __________.

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