
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
For lines $m$, $n$, and planes $\alpha$, $\beta$, $\gamma$, the following four propositions are given:  
(1) If $m \parallel \alpha$ and $m \perp n$, then $n \perp \alpha$.  
(2) If $m \perp \alpha$ and $m \perp n$, then $n \parallel \alpha$.  
(3) If $\alpha \perp \beta$ and $\gamma \perp \beta$, then $\alpha \parallel \gamma$.  
(4) If $m \perp \alpha$ and $m \parallel n$, and $n \subset \beta$, then $\alpha \perp \beta$.  
Among these, the correct proposition(s) is/are.

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