
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
If the sides $AB$, $BC$, $CA$ of an equilateral triangle are divided in the same ratio and we connect the division points, we obtain another equilateral triangle. In what ratio should the sides of the given triangle be divided so that the area of the triangle formed by the division points is minimized?

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