
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 $α$ and $β$, consider the following propositions:
- $(1)$ If $m \parallel β$, $n \parallel β$, $m \subset α$, $n \subset α$, then $α \parallel β$.
- $(2)$ If $m \perp β$, $n \perp β$, $m \subset α$, $n \not\subset α$, then $n \parallel α$.
- $(3)$ If $m \subset α$, $n \subset β$, $α \cap β = l$, and $m \perp l$, $n \perp l$, then $α \perp β$.
- $(4)$ If $m$ and $n$ are skew lines, $m \subset α$, $n \subset β$, and $m \parallel β$, $n \parallel α$, then $α \parallel β$.

The sequence number of the correct propositions is __________ (fill in the sequence number of all correct propositions).

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