
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 $m$, $n$, $l$ are three lines, and $\alpha$, $\beta$ are two planes, among the following statements, the correct ones are:

① If $l$ is perpendicular to two lines within $\alpha$, then $l \perp \alpha$;  
② If $l$ is parallel to $\alpha$, then there are infinitely many lines within $\alpha$ that are parallel to $l$;  
③ If $m \parallel \beta$, $m \subset \alpha$, $n \subset \beta$, then $m \parallel n$;  
④ If $m \perp \alpha$, $m \perp \beta$, then $\alpha \parallel \beta$.

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