
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
A closed eight-segment broken line (polyline) is drawn on the surface of a cube, with its vertices coinciding with the vertices of the cube.

What is the minimum number of segments of this broken line that can coincide with the edges of the cube?

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