
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 four propositions, the correct ones are:  
① The sufficient but not necessary condition for "lines a and b to be skew lines" is "lines a and b do not intersect";  
② The necessary and sufficient condition for "line l to be perpendicular to all lines in plane α" is "l is perpendicular to α";  
③ The sufficient but not necessary condition for "line a to be perpendicular to line b" is "a is perpendicular to the projection of b in plane α";  
④ The necessary but not sufficient condition for "line a to be parallel to plane β" is "line a is parallel to a line in plane β".

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