
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
We have an  $n \times n$  square divided into unit squares. Each side of unit square is called unit segment. Some isoceles right triangles of hypotenuse  $2$  are put on the square so all their vertices are also vertices of unit squares. For which  $n$  it is possible that every unit segment belongs to exactly one triangle(unit segment belongs to a triangle even if it's on the border of the triangle)?

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