
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
The masses of three iron balls are \( m_{1}=8 \text{ kg}, m_{2}=9 \text{ kg}, m_{3}=10 \text{ kg} \). They are placed at the vertices of an equilateral triangle (with sides \( a=1 \text{ m} \)). Where is their center of mass?

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