
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
Suppose $a$ and $b$ are two lines, and $\alpha$ and $\beta$ are two planes. Among the following four sets of conditions, identify all the sets that logically imply $a \perp b$ (perpendicular). (Fill in the sequence numbers)  
① $a \subset \alpha$, $b \parallel \beta$, $\alpha \perp \beta$;  
② $a \perp \alpha$, $b \perp \beta$, $\alpha \perp \beta$;  
③ $a \subset \alpha$, $b \perp \beta$, $\alpha \parallel \beta$;  
④ $a \perp \alpha$, $b \parallel \beta$, $\alpha \parallel \beta$.

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