
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 lines, $α$ and $β$ are planes, provide the correct proposition number(s) for the following:
\[① \begin{cases} m⊥α \\\\ m⊥n\\end{cases}⇒n/\\!/α\] \[② \begin{cases} m⊥β \\\\ n⊥β\\end{cases}⇒m/\\!/n\]  \[③ \begin{cases} m⊥α \\\\ m⊥β\\end{cases}⇒α/\\!/β\]  \[④ \begin{cases} m⊂α \\\\ n⊂β⇒m/\\!/n \\\\ α/\\!/β\\end{cases}\]

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