
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 $α$, $β$, and $γ$ are distinct planes, and $m$ and $n$ are distinct lines, the following four propositions are provided:

$①$ If $α ⟂ γ$ and $β ⟂ γ$, then $α // β$;
$②$ If $α ⟂ β$ and $β ⟂ γ$, then $α ⟂ γ$;
$③$ If $m ⟂ α$ and $α ⟂ β$, then $m // β$;
$④$ If $m ⟂ α$ and $n ⟂ α$, then $m // n$.

Determine the number of correct propositions.

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