
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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Each side of an equilateral triangle is divided into three equal parts, and the corresponding division points, taken in one direction, are connected. An inscribed circle with a radius of \( r = 6 \text{ cm} \) is placed inside the resulting equilateral triangle. Determine the sides of the triangles.

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