
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 three points A, B, C in space, two lines a, b, and a plane α, the following propositions are given: ① If A∈α, B∈α, and C∈AB, then C∈α; ② If A∉α and B∉α, then AB∥α; ③ If a⊥α and b⊥a, then b∥α. The number of correct propositions is.

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