
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 the following four propositions:  
① If line $a$ is contained in plane $\beta$, and $\alpha \parallel \beta$, then the distance between line $a$ and plane $\alpha$ is equal to the distance between plane $\alpha$ and plane $\beta$;  
② If two parallel lines are respectively contained in two parallel planes, then the distance between these two parallel lines is equal to the distance between these two parallel planes;  
③ If skew lines $a$ and $b$ are respectively contained in two parallel planes, then the distance between $a$ and $b$ is equal to the distance between these two planes;  
④ If point $A$ is in plane $\alpha$, and plane $\alpha \parallel$ plane $\beta$, then the distance from $A$ to plane $\beta$ is equal to the distance between plane $\alpha$ and plane $\beta$.  
Among these, the correct propositions are numbered as follows.

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