
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 that $m$ and $n$ are two different lines, and $α$ and $β$ are two different planes, the following propositions are provided:
1. $\begin{cases} \overset{m\perp \alpha }{m\perp n}\end{cases} \Rightarrow n\parallel\alpha$
2. $\begin{cases} \overset{m\perp \beta }{n\perp \beta }\end{cases} \Rightarrow n\parallel m$
3. $\begin{cases} \overset{m\perp \alpha }{m\perp \beta }\end{cases} \Rightarrow \beta\parallel\alpha$
4. $\begin{cases} m\subset\alpha \\ n\subset\beta \\ \alpha\parallel\beta\end{cases} \Rightarrow m\parallel n$

Identify the correct proposition number(s).

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