
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
Petya marked a point \( \mathrm{X} \) on the edge \( \mathrm{AB} \) of the cube \( \mathrm{ABCDA1B1C1D1} \) such that it divides the edge \( \mathrm{AB} \) in the ratio \( 1:2 \), starting from vertex \( \mathrm{A} \). Give an example of how Petya can mark points \( \mathrm{Y} \) and \( \mathrm{Z} \) on the edges \( \mathrm{CC1} \) and \( \mathrm{A1D1} \) respectively, so that the triangle \( \mathrm{XYZ} \) is equilateral. Justify the answer.

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