
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 that $m$ and $l$ are lines, and $\alpha$ and $\beta$ are planes, consider the following propositions:  
(1) If $l$ is perpendicular to two intersecting lines within $\alpha$, then $l \perp \alpha$;  
(2) If $l$ is parallel to $\alpha$, then $l$ is parallel to all lines within $\alpha$;  
(3) If $m \subset \alpha$, $l \subset \beta$, and $l \perp m$, then $\alpha \perp \beta$;  
(4) If $l \subset \beta$, and $l \perp \alpha$, then $\alpha \perp \beta$;  
(5) If $m \subset \alpha$, $l \subset \beta$, and $\alpha \parallel \beta$, then $l \parallel m$.  
Among these propositions, the correct ones are \_\_\_\_\_\_.

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