
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 different lines, and $\alpha$, $\beta$, $\gamma$ be different planes. There are the following four propositions:  
① If $\alpha \parallel \beta$ and $\alpha \parallel \gamma$, then $\beta \parallel \gamma$.  
② If $\alpha \perp \beta$ and $m \parallel \alpha$, then $m \perp \beta$.  
③ If $m \subset \alpha$, $n \perp \beta$, and $\alpha \parallel \beta$, then $m \perp n$.  
④ If $m \parallel n$ and $n \subset \alpha$, then $m \parallel \alpha$.  
Among these, the numbers of the true propositions are.

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