
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 $\alpha$ and $\beta$ are two different planes, and $m$ and $n$ are two different lines, consider the following propositions:  
① If $m \parallel \alpha$, $n \parallel \alpha$, then $m \parallel n$;       ② If $m \perp \alpha$, $n \perp \alpha$, then $m \parallel n$;  
③ If $m \parallel \alpha$, $\alpha \cap \beta = n$, then $m \parallel n$;    ④ If $m \perp \alpha$, $m \parallel n$, $n \subset \beta$, then $\alpha \perp \beta$.  
Among these propositions, the numbers of the true propositions are    ．(Write down the numbers of all true propositions)

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