
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) If a line is parallel to another line, then it is also parallel to any plane that passes through the other line;  
(2) If a line is parallel to a plane, then this line does not have any common points with all the lines within this plane, thus this line is parallel to all the lines within this plane;  
(3) If line $l$ is not parallel to plane $\alpha$, then $l$ is not parallel to any line within $\alpha$;  
(4) A line that is parallel to countless lines within a plane must be parallel to the plane.  
The number of correct propositions is.

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