
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
Among the following conditions, the ones that can determine if plane $\alpha$ is parallel to plane $\beta$ are     . (Write down all the correct condition numbers)  
① There are infinitely many lines within $\alpha$ that are parallel to $\beta$;  
② Any line within $\alpha$ is parallel to $\beta$;  
③ Line $a \subset \alpha$, line $b \subset \beta$, and $a \parallel \beta$, $b \parallel \alpha$;  
④ $a \perp \alpha$, $b \perp \beta$, and $a \parallel b$.

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