
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 $m$ and $n$ be two different lines, and $\alpha$, $\beta$, $\gamma$ be three different planes. Consider the following four propositions:  
1. If $\alpha \cap \beta = m$, $n \parallel \beta$, $n \parallel \alpha$, then $m \parallel n$;  
2. If $\alpha \perp \beta$, $n \perp \alpha$, then $n \parallel \beta$;  
3. If $m \subset \alpha$, $n \subset \beta$, $m \perp n$, then $\alpha \perp \beta$;  
4. If $m \perp \alpha$, $n \perp \alpha$, then $m \parallel n$;  
Among these propositions, the correct ones are ____. (Fill in the numbers of the correct propositions)

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