
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
Among the following propositions, the correct ones are:  
(1) Skew lines refer to two lines in space that do not have a common point;  
(2) If lines $a$ and $b$ are skew, and $a \perp$ plane $\alpha$, then $b$ is not perpendicular to plane $\alpha$;  
(3) If skew lines $a$ and $b$ satisfy $a \parallel$ plane $\alpha$, $b \parallel$ plane $\alpha$, and $l \perp$ plane $\alpha$, then $l$ is perpendicular to both $a$ and $b$;  
(4) The projections of two skew lines onto the same plane cannot be two parallel lines.

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