
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 $α$ and $β$ are two non-coinciding planes, and $m$ and $n$ are two different lines, identify the correct statement(s) from the following propositions (fill in the serial number):

$①$ If $α \parallel β$ and $m \subset α$, then $m \parallel β$;  
$②$ If $m \parallel α$ and $n \subset α$, then $m \parallel n$;  
$③$ If $α \perp β$ and $α \cap β = n$, and $m \perp n$, then $m \perp β$;  
$④$ If $n \perp α$ and $n \perp β$ and $m \perp α$, then $m \perp β$.

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