
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
Let $m$ and $n$ be two different lines, and $\alpha$, $\beta$, $\gamma$ be three different planes. Given the following four propositions:  
① If $m \perp \alpha$ and $n \parallel \alpha$, then $m \perp n$;  
② If $\alpha \perp \gamma$, $\beta \perp \gamma$, and $\alpha \cap \beta = m$, then $m \perp \gamma$;  
③ If $m \parallel \alpha$ and $n \subset \alpha$, then $m \parallel n$;  
④ If $\alpha \perp \beta$, $\alpha \cap \beta = n$, and $m \perp n$, then $m \perp \beta$  
Among these propositions, the correct ones are \_\_\_\_\_\_.

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