
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 $\alpha$ and $\beta$ be two distinct planes, and let $m$, $n$, and $l$ be three distinct lines. Consider the following statements, and identify the correct ones:

① If $m \perp n$ and $m \perp \alpha$, then $n \parallel \alpha$;  
② If $n \subset \alpha$, $m \subset \beta$, and $\alpha$ intersects $\beta$ non-perpendicularly, then $n$ is not perpendicular to $m$;  
③ If $\alpha \perp \beta$, $\alpha \cap \beta = m$, $n \subset \alpha$, and $m \perp n$, then $n \perp \beta$;  
④ If $m$ is a skew line to plane $\alpha$, $n$ is the projection of $m$ onto plane $\alpha$, and if $l \perp n$, then $l \perp m$.

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