
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 the following propositions:  
(1) Three parallel lines are coplanar;  
(2) In space, only one line parallel to a given line can be drawn through a point not on the line;  
(3) Two planes that have three common points coincide;  
(4) If lines a, b, c satisfy a⊥b, a⊥c, then b∥c.  
The number of correct propositions is.

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