
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 propositions:  
① Skew lines refer to lines in space that are neither parallel nor intersecting;  
② For two skew lines $a$ and $b$, if $a$ is parallel to plane $\alpha$, then $b$ is not parallel to plane $\alpha$;  
③ For two skew lines $a$ and $b$, if $a$ is perpendicular to plane $\alpha$, then $b$ is not perpendicular to plane $\alpha$;  
④ The projections of two skew lines onto the same plane cannot be two parallel lines.  
Among the above propositions, the numbers of the true propositions are.

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