
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 serial numbers of all correct propositions are __________.

① Plane $\alpha$ and plane $\beta$ intersect, and they only have a finite number of common points;  
② Through a line and a point not on the line, there is exactly one plane;  
③ Through two intersecting lines, there is exactly one plane;  
④ If two planes have three non-collinear common points, then the two planes coincide;  
⑤ A quadrilateral determines a plane.

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