
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 that $m$ and $n$ are two different lines, and $\alpha$, $\beta$, $\gamma$ are three different planes, there are the following four propositions:  
1. If $m \perp \alpha$ and $m \perp \beta$, then $\alpha \parallel \beta$;  
2. If $\alpha \parallel \gamma$ and $\beta \parallel \gamma$, then $\alpha \parallel \beta$;  
3. If $m \subset \alpha$ and $n \subset \beta$ and $m \parallel n$, then $\alpha \parallel \beta$;  
4. If $m$ and $n$ are skew lines, and $m \subset \alpha$, $n \subset \beta$, $n \nparallel \alpha$, $m \nparallel \beta$, then $\alpha \parallel \beta$.  
Among these propositions, the correct ones are __________. (Fill in the numbers of all correct propositions)

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