
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
$\alpha$ and $\beta$ are two different planes, and $m$ and $n$ are two different lines outside of planes $\alpha$ and $\beta$. Given four statements: ① $m \perp n$, ② $\alpha \perp \beta$, ③ $n \perp \beta$, ④ $m \perp \alpha$. Using three of these statements as conditions and the remaining one as a conclusion, write down a proposition that you think is correct: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (just fill in the number).

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