
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 propositions: (1) If point P is not on plane α, and points A, B, and C are all on plane α, then the four points P, A, B, and C are not on the same plane; (2) Three straight lines that intersect each other are on the same plane; (3) A quadrilateral with two pairs of opposite sides being equal is a parallelogram. Determine the number of correct propositions.

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