
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 $l$, $m$, $n$ be three different lines, and $\alpha$, $\beta$, $\gamma$ be three different planes. Below are four propositions:  
① If $l \parallel \beta$, $\alpha \parallel \beta$, then $l \parallel \alpha$;  
② If $l \parallel n$, $m \parallel n$, then $l \parallel m$;  
③ If $\alpha \perp \beta$, $l \parallel \alpha$, then $l \perp \beta$;  
④ If $l \perp \alpha$, $m \perp \beta$, $\alpha \perp \beta$, then $l \perp m$.  
Among these, the false propositions are numbered as     .

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