
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 $l$ is perpendicular to two intersecting lines within $\alpha$, then $l \perp \alpha$;  
② If $l \parallel \alpha$, 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 $l \subset \beta$, $l \perp \alpha$, then $\alpha \perp \beta$;  
⑤ If $m \subset \alpha$, $l \subset \beta$ and $\alpha \parallel \beta$, then $m \parallel l$.  
The correct propositions are numbered as     . (Fill in the numbers of all correct propositions)

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