
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 two lines $a$ and $b$, and two different planes $\alpha$ and $\beta$, the number of correct statements among the following four is __________.  
① If $a \perp b$ and $a \perp \alpha$, then $b \parallel \alpha$  
② If $\alpha \perp \beta$ and $a \parallel \alpha$, then $a \perp \beta$  
③ If $a \perp \beta$ and $\alpha \perp \beta$, then $a \parallel \alpha$  
④ If $a \perp b$, $a \perp \alpha$, and $b \perp \beta$, then $\alpha \perp \beta$

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