
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 $r$ be planes, and $m$, $n$, and $l$ be lines. Consider the following four sets of conditions:
1. $\alpha \perp \beta$, $\alpha \cap \beta = l$, $m \perp l$
2. $\alpha \cap r = m$, $\alpha \perp r$, $\beta \perp r$
3. $\alpha \perp r$, $\beta \perp r$, $m \perp \alpha$
4. $n \perp \alpha$, $n \perp \beta$, $m \perp \alpha$

The sufficient condition for $m \perp \beta$ is.

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