
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 four propositions: ① If segment AB is in plane $\alpha$, then line AB is not in $\alpha$; ② If two planes have one common point, then they must have infinitely many common points; ③ Three parallel lines are coplanar; ④ Two planes that have three common points coincide. Among these, the number of correct propositions is.

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