
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 a cube with side length \( n \) cm, we have a long piece of insulating tape with a width of 1 cm. The task is to cover the entire cube with the tape. The tape can transition freely across edges to different faces, but on any given face, it must run straight parallel to an edge and cannot hang off the side. Into how many pieces must the tape be cut to cover the cube?

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