
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 polygonal line connects two opposite vertices of a cube with side length 2. Each segment of the line has length 3, and each vertex of the line lies on the faces or edges of the cube. What is the smallest number of segments the line can have?

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