
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 $β$, determine which of the following conditions can imply that $α$ is parallel to $β$. (Select the appropriate option(s))

$①$ There exists a line $a$ such that $a ⊥ α$ and $a ⊥ β$;

$②$ There exists a plane $γ$ such that $γ ⊥ α$ and $γ ⊥ β$;

$③$ There exist two parallel lines $a$ and $b$ such that $a ⊂ α$, $b ⊂ β$, $a$ is parallel to $β$, and $b$ is parallel to $α$;

$④$ There exist two skew lines $a$ and $b$ such that $a ⊂ α$, $b ⊂ β$, $a$ is parallel to $β$, and $b$ is parallel to $α$.

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