
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
(5 points) Let $\alpha$, $\beta$, $\gamma$ be three distinct planes, and $l$ be a line. Consider the following four propositions:  
① If $\alpha \perp \beta$ and $l \perp \beta$, then $l \parallel \alpha$;  
② If $l \perp \alpha$ and $l \parallel \beta$, then $\alpha \perp \beta$;  
③ If there are two points on $l$ that are equidistant from $\alpha$, then $l \parallel \alpha$;  
④ If $\alpha \perp \beta$ and $\alpha \parallel \gamma$, then $\gamma \perp \beta$.  
The correct propositions are numbered as $\boxed{\text{②④}}$.

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