
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 that $m$ and $n$ are two non-coincident lines, and $\alpha$ and $\beta$ are two non-coincident planes, among the following statements, the true ones are:  
① If both $m$ and $n$ are parallel to plane $\alpha$, then $m$ and $n$ must not intersect;  
② If both $m$ and $n$ are perpendicular to plane $\alpha$, then $m$ and $n$ must be parallel lines;  
③ Given that $\alpha$ and $\beta$ are perpendicular to each other, and $m$ and $n$ are perpendicular to each other, if $m \perp \alpha$, then $n \perp \beta$;  
④ If the projections of $m$ and $n$ on plane $\alpha$ are perpendicular to each other, then $m$ and $n$ are perpendicular to each other.

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