
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 that $l$ and $m$ are two different lines, and $\alpha$ and $\beta$ are two different planes, there are the following four propositions:  
1. If $l \subset \beta$, and $\alpha \perp \beta$, then $l \perp \alpha$;  
2. If $l \perp \beta$, and $\alpha \parallel \beta$, then $l \perp \alpha$;  
3. If $l \perp \beta$, and $\alpha \perp \beta$, then $l \parallel \alpha$;  
4. If $\alpha \cap \beta = m$, and $l \parallel m$, then $l \parallel \alpha$.  

Among these propositions, the numbers of the true propositions are.

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