
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 two skew lines \(m\) and \(n\) in plane \(\alpha\), where \(m\) is parallel to \(n\), what could be the set of points in plane \(\alpha\) that are equidistant from lines \(m\) and \(n\) by a distance \(d\)? The possible sets of points are: (1) a straight line; (2) a point; (3) two points; (4) an empty set. Which of these is correct (write all correct answer numbers)? ______ .

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