
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
Three dice are rolled, and the numbers that appear are used to place balls into bins. Each die corresponds to a ball and the bin number is determined by the square of the number on the die. Two balls are considered to be evenly spaced if the difference between their bin numbers is a multiple of 4. What is the probability that, when three fair six-sided dice are rolled, the balls end up in evenly spaced bins?
A) $\frac{1}{36}$  
B) $\frac{1}{72}$  
C) $\frac{1}{108}$  
D) $\frac{1}{144}$

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