
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 $α$ and $β$ be two planes, and let $m$ and $n$ be two lines. Consider the following four propositions:
1. If plane $α$ is parallel to plane $β$ ($α \parallel β$) and line $m$ is contained in plane $α$ ($m \subset α$), then line $m$ is parallel to plane $β$ ($m \parallel β$);
2. If line $m$ is perpendicular to plane $α$ ($m \perp α$) and line $m$ is perpendicular to line $n$ ($m \perp n$), then line $n$ is parallel to plane $α$ ($n \parallel α$);
3. If line $m$ is perpendicular to plane $α$ ($m \perp α$) and line $n$ is parallel to plane $α$ ($n \parallel α$), then line $m$ is perpendicular to line $n$ ($m \perp n$);
4. If line $m$ is perpendicular to line $n$ ($m \perp n$), line $m$ is perpendicular to plane $α$ ($m \perp α$), and line $n$ is parallel to plane $β$ ($n \parallel β$), then planes $α$ and $β$ are perpendicular to each other ($α \perp β$).
Identify the correct propositions. (Fill in the correct proposition numbers)

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