
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 $\alpha$ and $\beta$ be two different planes, and let $m$ and $n$ be two distinct lines outside of planes $\alpha$ and $\beta$. Given four assertions:
(1) $m \perp n$
(2) $\alpha \perp \beta$
(3) $n \perp \beta$
(4) $m \perp \alpha$
Based on three of these assertions as premises, with the remaining as a conclusion, write down a proposition that you consider to be correct.

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