
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 $\alpha$ and $\beta$ are two different planes, the following four conditions are given:  
1. There exists a line $a$, such that $a \perp \alpha$ and $a \perp \beta$;  
2. There exists a plane $\gamma$, such that $\gamma \perp \alpha$ and $\gamma \perp \beta$;  
3. There exist two parallel lines $a$ and $b$, where $a \subset \alpha$, $b \subset \beta$, $a \parallel \beta$, and $b \parallel \alpha$;  
4. There exist two skew lines $a$ and $b$, where $a \subset \alpha$, $b \subset \beta$, $a \parallel \beta$, and $b \parallel \alpha$.  
Among these, the sufficient conditions for plane $\alpha \parallel$ plane $\beta$ are \_\_\_\_\_\_\_\_(fill in all required sequence numbers).

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