
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
In an equilateral triangle, mark each point whose distance from the nearest vertex is less than the distance from the centroid. What percentage of the area of the equilateral triangle do the points with this property occupy?

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