
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
(2009 Jiangsu Exam) Let $\alpha$ and $\beta$ be two distinct planes. Consider the following statements:

(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 at line $l$, if there is a line within $\alpha$ that is perpendicular to $l$, then $\alpha$ and $\beta$ are perpendicular;

(4) The necessary and sufficient condition for a line $l$ to be perpendicular to plane $\alpha$ is for $l$ to be perpendicular to two lines within $\alpha$.

Among the statements above, list the numbers of the true statements.

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