
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 $800$ students at Queen High School are divided into four groups of equal size for lunch. Each group has lunch at a different time. A computer randomly assigns each student to one of four lunch groups. Determine the probability that three friends, Alex, Bailey, and Casey, will be assigned to the same lunch group.
A) $\frac{1}{64}$
B) $\frac{1}{32}$
C) $\frac{1}{16}$
D) $\frac{1}{8}$
E) $\frac{1}{4}$

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