
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 \( a \) and \( b \) as two lines, and \( \alpha \) and \( \beta \) as two planes, among the following four sets of conditions, all that can lead to the conclusion that \( a \) is perpendicular to \( b \) are __________ (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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