
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 $\alpha$ be a plane in space, and $l$, $m$, $n$ be three different lines. Then, the correct statement(s) is/are \_\_\_\_\_\_ ;  
① If $m \subset \alpha$, $n \subset \alpha$, $l \perp m$, $l \perp n$, then $l \perp \alpha$; ② If $m \subset \alpha$, $n \subset \alpha$, then $l \parallel m$;  
③ If $l \parallel m$, $m \perp \alpha$, $n \perp \alpha$, then $l \parallel n$;      ④ If $l \perp m$, $l \perp n$, then $n \parallel m$.

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