
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
King High School has 900 students, who are randomly assigned into four lunch groups of equal size. If three particular friends, Dani, Emma, and Fay, are among these students, what is the probability that all three will be assigned to the same lunch group?
A) $\frac{1}{36}$  
B) $\frac{1}{24}$  
C) $\frac{1}{16}$  
D) $\frac{1}{12}$  
E) $\frac{1}{8}$

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