
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 three non-coincident straight lines and two non-coincident planes, the following propositions are given:  
① If $m \parallel n$, and $n \subset \alpha$, then $m \parallel \alpha$; ② If $l \perp \alpha$, $m \perp \beta$, and $l \parallel m$, then $\alpha \parallel \beta$; ③ If $m \subset \alpha$, $n \subset \alpha$, $m \parallel \beta$, and $n \parallel \beta$, then $\alpha \parallel \beta$; ④ If $\alpha \perp \beta$, $\alpha \cap \beta = m$, and $n \subset \beta$, $n \perp m$, then $n \perp \alpha$. Among these, the correct propositions are.

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