
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 two distinct lines $m$ and $n$, and two distinct planes $\alpha$ and $\beta$, consider the following four propositions:
1. If $m \subset \beta$ and $\alpha \perp \beta$, then $m \perp \alpha$;
2. If $\alpha \! \! \! / / \! \beta$ and $m \subset \alpha$, then $m \! \! \! / / \! \beta$;
3. If $n \perp \alpha$, $n \perp \beta$, and $m \perp \alpha$, then $m \perp \beta$;
4. If $m \! \! \! / / \! \alpha$ and $m \! \! \! / / \! \beta$, then $\alpha \! \! \! / / \! \beta$.
Determine the sequence number(s) of the correct proposition(s).

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