
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 $m$ and $n$ be two different lines, and $\alpha$ be a plane. There are the following four propositions:  
① If $m \perp n$ and $m \subset \alpha$, then $n \perp \alpha$;  
② If $m \perp \alpha$ and $n \parallel m$, then $n \perp \alpha$;  
③ If $n \parallel \alpha$ and $m \subset \alpha$, then $n \parallel m$;  
④ If $m \parallel \alpha$ and $n \parallel \alpha$, then $m \parallel n$.  
Among these propositions, the true ones are (write down the numbers of all true propositions).

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