
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

Cut a given square into two parts of equal area using a broken line (polyline) so that each segment of the broken line is parallel to a side or a diagonal of the square. Additionally, the sum of the lengths of segments parallel to the sides should equal the side length, and the sum of the lengths of segments parallel to the diagonals should equal the diagonal length. What is the minimum number of segments that such a broken line can have?

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