
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 square is divided into $n^{2}$ equal smaller squares. It is known that a certain polyline passes through the centers of all these smaller squares (the polyline may intersect itself). What is the minimum number of segments in this polyline?

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