
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 $m$ is two different lines, $\alpha$, $\beta$ are two different planes, there are four propositions as follows:

$①$ If $l \subset \beta$, and $\alpha \bot \beta$, then $l \bot \alpha$;

$②$ If $l \bot \beta$, and $\alpha // \beta$, then $l \bot \alpha$;

$③$ If $l \bot \beta$, and $\alpha \bot \beta$, then $l // \alpha$;

$④$ If $\alpha \cap \beta = m$, and $l // m$, then $l // \alpha$.

The sequence numbers of all correct propositions are $\_\_\_\_\_\_\_\_\_\_.$

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