
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 non-intersecting planes $α$ and $β$, and two non-intersecting lines $m$ and $n$. The following four propositions are provided:
1) If $n⊂α$, $n$ is parallel to $β$, and $α∩β=m$, then $n$ is parallel to $m$;
2) If $m⊂α$, $n⊂α$, $m$ is parallel to $β$, and $n$ is parallel to $β$, then $α$ is parallel to $β$;
3) If $α⊥β$, $α∩β=m$, $n⊂α$, and $n⊥m$, then $n⊥β$;
4) If $m⊥α$, $α⊥β$, and $m$ is parallel to $n$, then $n$ is parallel to $β$.
Identify the correct proposition number(s).

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