
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
Let $l$ and $m$ be two different lines, and $\alpha$ and $\beta$ be two non-coincident planes. Given the following four propositions:

$①$ If $\alpha \parallel \beta$, $l \perp \alpha$, then $l \perp \beta$;  
$②$ If $l \parallel m$, $l \subset \alpha$, $m \subset \beta$, then $\alpha \parallel \beta$;  

$③$ If $m \perp \alpha$, $l \perp m$, then $l \parallel \alpha$;  
$④$ If $\alpha \perp \beta$, $l \subset \alpha$, $m \subset \beta$, then $l \perp m$.

Among these, the true proposition(s) is/are ______.

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