
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 $m$ and $l$ are lines, and $\alpha$, $\beta$, $\gamma$ are planes, consider the following propositions:  
① If $\beta \cap \gamma = l$, $l \parallel \alpha$, $m \subset \alpha$, and $m \perp \gamma$, then $\alpha \perp \gamma$ and $m \parallel \beta$;  
② If $l \subset \beta$ and $l \perp \alpha$, then $\alpha \perp \beta$;  
③ If $\beta \cap \gamma = l$, $l \parallel \alpha$, $m \subset \alpha$ and $m \perp \gamma$, then $\alpha \perp \gamma$ and $l \perp m$;  
④ If $m \subset \alpha$, $l \subset \beta$, and $\alpha \parallel \beta$, then $m \parallel l$;  
⑤ If $m \parallel \alpha$, $m \subset \beta$, and $\alpha \cap \beta = l$, then $m \perp l$,  
Among these, the correct propositions are     ．

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