
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 a line is parallel to a line within a plane, then this line is parallel to the plane;  
② Two planes perpendicular to the same line are parallel to each other;  
③ If a line is perpendicular to countless lines within a plane, then this line is perpendicular to the plane;  
④ If there is a line within a plane that is perpendicular to another plane, then these two planes are perpendicular to each other.  
The correct proposition numbers are __________.

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