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

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