
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 $\alpha$, $\beta$, and $\gamma$ be planes, and let $m$, $n$, and $l$ be lines. Consider the following conditions:
1. $\alpha \perp \beta$, $\alpha \cap \beta = l$, $m \perp l$;
2. $\alpha \cap \gamma = m$, $\alpha \perp \beta$, $\gamma \perp \beta$;
3. $\alpha \perp \gamma$, $\beta \perp \gamma$, $m \perp \alpha$;
4. $n \perp \alpha$, $n \perp \beta$, $m \perp \alpha$.

Among these conditions, the sufficient conditions for $m \perp \beta$ are __________ (fill in all correct sequence numbers).

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