
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
Given two lines $m$, $n$ and two planes $\alpha$, $\beta$, the correctness of the following four propositions is to be determined:  
① If $\alpha \cap \beta = m$, and $n \subset \alpha$, then $m \parallel n$ or $m$ intersects $n$;  
② If $\alpha \parallel \beta$, $m \subset \alpha$, and $n \subset \beta$, then $m \parallel n$;  
③ If $m \parallel n$ and $m \parallel \alpha$, then $n \parallel \alpha$;  
④ If $\alpha \cap \beta = m$ and $m \parallel n$, then $n \parallel \beta$ and $n \parallel \alpha$. The correct proposition(s) is/are \_\_\_\_\_\_.

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