
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 $n$ represent lines, and $\alpha$, $\beta$, $\gamma$ represent planes. Consider the following four propositions:  
(1) $\alpha \cap \beta = m$, $n \subset \alpha$, $n \perp m$, then $\alpha \perp \beta$  
(2) $\alpha \perp \beta$, $\alpha \cap \gamma = m$, $\beta \cap \gamma = n$, then $n \perp m$  
(3) $\alpha \perp \beta$, $\alpha \perp \gamma$, $\beta \cap \gamma = m$, then $m \perp \alpha$  
(4) $m \perp \alpha$, $n \perp \beta$, $m \perp n$, then $\alpha \perp \beta$  
The correct propositions are:

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