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

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