
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 $\alpha$ and $\beta$ be two non-coincident planes, and $m$ and $n$ be two non-coincident lines. Consider the following four propositions:  
① If $m \perp n$, $m \perp \alpha$, and $n \nsubseteq \alpha$ then $n \parallel \alpha$;  
② If $\alpha \perp \beta$, $\alpha \cap \beta = m$, $n \subset \alpha$, and $n \perp m$, then $n \perp \beta$;  
③ If $m \perp n$, $m \parallel \alpha$, and $n \parallel \beta$, then $\alpha \perp \beta$;  
④ If $n \subset \alpha$, $m \subset \beta$, $\alpha$ intersects $\beta$ and they are not perpendicular, then $n$ and $m$ are not perpendicular.  
Among these, the serial numbers of all true propositions are $\boxed{\text{①②}}$.

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