
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
For tetrahedron ABCD, which of the following propositions is correct? (Write down all correct propositions.)  
① The lines containing opposite edges AB and CD are skew lines; ② If $AB \perp CD$ and $BC \perp AD$, then $AC \perp BD$; ③ If the midpoints of the three pairs of opposite edges are connected, the resulting three segments intersect at one point.

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