
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]


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An equilateral triangle is divided into smaller equilateral triangles with side length 1 by lines parallel to its sides, dividing each side into \( n \) parts (in the diagram \( n = 5 \)). 

What is the maximum number of length 1 segments, with endpoints at the vertices of these smaller triangles, that can be marked so that no triangle is formed where all sides are marked segments?

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