
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 $l$, $m$, $n$ represent different lines, and $\alpha$, $\beta$, $\gamma$ represent different planes. Consider the following four propositions:  
① If $m \parallel l$ and $m \perp \alpha$, then $l \perp \alpha$.  
② If $m \parallel l$ and $m \parallel \alpha$, then $l \parallel \alpha$.  
③ If $\alpha \cap \beta = l$, $\beta \cap \gamma = m$, $\gamma \cap \alpha = n$, then $l \parallel m \parallel n$.  
④ If $\alpha \cap \beta = l$, $\beta \cap \gamma = m$, $\gamma \cap \alpha = n$ and $n \parallel \beta$, then $l \parallel m$.  
Among these propositions, the correct ones are \_\_\_\_\_\_.

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