
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
Let $\alpha$ and $\beta$ be two non-coincident planes, and consider the following propositions:  
(1) If two intersecting lines within plane $\alpha$ are parallel to two lines within plane $\beta$, then $\alpha$ is parallel to $\beta$;  
(2) If a line $l$ outside of plane $\alpha$ is parallel to a line within $\alpha$, then $l$ is parallel to $\alpha$;  
(3) Suppose $\alpha$ and $\beta$ intersect along line $l$, if there is a line within $\alpha$ that is perpendicular to $l$, then $\alpha$ and $\beta$ are perpendicular;  
(4) If $l$ is perpendicular to two lines within $\alpha$, then line $l$ is perpendicular to $\alpha$. Among these propositions, the number of incorrect ones is

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