
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 three propositions:  
① If lines a and b are skew lines, and lines c and d intersect with a and b at four distinct points E, F, G, H, respectively, then c and d are skew lines;  
② If a line is parallel to one of two skew lines, then it cannot be parallel to the other line;  
③ If a line intersects with two skew lines, then they can determine two planes.  
Among these, the true propositions are numbered as     .

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