
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 $l$, $m$, $n$ be three different lines, and $a$ be a plane. Consider the following statements:  
① If $l \perp a$, then $l$ intersects $a$;  
② If $m \subset a$, $n \subset a$, $l \perp m$, $l \perp n$, then $l \perp a$;  
③ If $l \parallel m$, $m \parallel n$, $l \perp a$, then $n \perp a$;  
④ If $l \parallel m$, $m \perp a$, $n \perp a$, then $l \parallel n$.  
Among these statements, the correct ones are.

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