
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:  
① If there are infinitely many points on line $l$ that are not within plane $\alpha$, then $l$ is parallel to $\alpha$;  
② If line $l$ is parallel to plane $\alpha$, then it is parallel to any line within the plane;  
③ If one of two parallel lines is parallel to a plane, then the other line is also parallel to this plane;  
④ If line $l$ is parallel to plane $\alpha$, then it has no common points with any line within the plane.  
The correct proposition numbers are __________ (Note: Fill in the numbers of the propositions you think are correct).

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