
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
Given $m$ and $n$ represent different lines, and $\alpha$, $\beta$, $\gamma$ represent different planes.  
① If $\alpha \cap \beta = m$, $n \subset \alpha$, $n \perp m$, then $\alpha \perp \beta$.  
② If $\alpha \perp \beta$, $\alpha \cap \gamma = m$, $\beta \cap \gamma = n$, then $n \perp m$.  
③ If $\alpha \perp \beta$, $\alpha \perp \gamma = m$, $\beta \cap \gamma = m$. Then $m \perp \alpha$.  
④ If $m \perp \alpha$, $n \perp \beta$, $m \perp n$, then $\alpha \perp \beta$.  
Among the above four propositions, the true propositions are.

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