
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 two different lines $m$ and $n$, and a plane $\alpha$. Consider the following three propositions:  
① If $m \perp \alpha$ and $n \perp \alpha$, then $m \parallel n$;  
② If $m \parallel \alpha$ and $n \parallel \alpha$, then $m \parallel n$;  
③ If $m \parallel \alpha$ and $n \perp \alpha$, then $m \perp n$.  
Among these, the true propositions are numbered as follows: (Write down the numbers of all true propositions)

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