
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 propositions:  
① If plane $\alpha \parallel$ plane $\beta$, and $AB$, $CD$ are segments between $\alpha$ and $\beta$, if $AB \parallel CD$, then $AB=CD$;  
② If $a$, $b$ are skew lines, and $b$, $c$ are skew lines, then $a$, $c$ must be skew lines;  
③ Through any point in space, two lines can be drawn perpendicular to a known plane $\alpha$;  
④ If plane $\alpha \parallel$ plane $\beta$, $P \in \alpha$, $PQ \parallel \beta$, then $PQ \subset \alpha$;  
⑤ If point $P$ is equidistant from the three vertices of a triangle, then the projection of point $P$ onto the plane of the triangle is the circumcenter of the triangle;  
⑥ If $a$, $b$ are two skew lines, and $P$ is a point in space, a plane can always be drawn through $P$ that is perpendicular to one of $a$, $b$ and parallel to the other.  
The correct propositions are    .

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