
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 $l$ and $m$ be two different lines, and $\alpha$ be a plane. Among the following propositions, the correct ones are:

① If $l \perp$ plane $\alpha$, $m \perp$ plane $\alpha$, then $l \parallel m$;  
② If $l \perp$ plane $\alpha$, $m \subset$ plane $\alpha$, then $l \perp m$;  
③ If $l \parallel$ plane $\alpha$, $l \parallel m$, then $m \parallel$ plane $\alpha$;  
④ If $l \parallel$ plane $\alpha$, $m \parallel$ plane $\alpha$, then $l \parallel m$.

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