
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 lines $m$, $n$, and planes $\alpha$, $\beta$, consider the following propositions:  
① If $m \perp \alpha$, $n \perp \beta$ and $m \perp n$, then $\alpha \perp \beta$  
② If $m \parallel \alpha$, $n \parallel \beta$ and $m \parallel n$, then $\alpha \parallel \beta$  
③ If $m \perp \alpha$, $n \parallel \beta$ and $m \perp n$, then $\alpha \perp \beta$  
④ If $m \perp \alpha$, $n \parallel \beta$ and $m \parallel n$ then $\alpha \parallel \beta$, the number of correct propositions is.

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