
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 $n$ be two different lines, and $\alpha$, $\beta$, $\gamma$ be three different planes. Consider the following propositions:  
① If $m \subset \beta$ and $\alpha \perp \beta$, then $m \perp \alpha$;  
② If $m \parallel \alpha$ and $m \perp \beta$, then $\alpha \perp \beta$;  
③ If $\alpha \perp \beta$ and $\alpha \perp \gamma$, then $\beta \perp \gamma$;  
④ If $\alpha \cap \gamma = m$ and $\beta \cap \gamma = n$, and $m \parallel n$, then $\alpha \parallel \beta$.  
Among the propositions above, the true ones are numbered as $\boxed{\text{②}}$ (List all the numbers of the true propositions).

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