
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
In the plane of a square \(ABCD\), construct a line such that the perpendicular projections of the vertices of the square onto this line are arranged so that three consecutive distances between these projection points are equal.

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