
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 two different lines $m$ and $l$, and two different planes $\alpha$ and $\beta$, consider the following propositions:  
(1) If $m \subset \alpha$, $l \subset \beta$ and $\alpha \parallel \beta$, then $m \parallel l$;  
(2) If $l \subset \beta$, $l \perp \alpha$, then $\alpha \perp \beta$;  
(3) If $l \parallel \alpha$, then $l$ is parallel to all lines within $\alpha$;  
(4) If $l \perp \alpha$, $m \perp \beta$, $l \perp m$, then $\alpha \perp \beta$;  
(5) If the projections of $l$ and $m$ within plane $\alpha$ are perpendicular to each other, then $l \perp m$.  
Among these propositions, the correct ones are (Fill in the numbers of all correct propositions).

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