
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
Regarding the non-coincident lines $m$, $n$ and planes $\alpha$, $\beta$, which of the following propositions are true? (Fill in the serial numbers of all true propositions)

① If $m \parallel \alpha$, $n \parallel \beta$, $\alpha \parallel \beta$, then $m \parallel n$.  
② If $m \parallel n$, $m \subset \alpha$, $n \perp \beta$, then $\alpha \perp \beta$.  
③ If $\alpha \cap \beta = m$, $m \parallel n$, then $n \parallel \alpha$, $n \parallel \beta$;  
④ If $\alpha \cap \beta = m$, $m \perp n$, then $n \perp \alpha$, $n \perp \beta$.

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