
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 regular triangle \( \triangle ABC \) with side length 3 is divided into three equal parts on each side. Parallel lines to each side are drawn through these division points, creating a total of 10 intersection points within and on the edges of the triangle, known as grid points. Determine the minimum number \( n \) of grid points that must be selected such that among these \( n \) points, there are always three points that form an isosceles triangle (including equilateral triangles).

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