
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 Middle School now has 800 students who are divided into four groups of equal size for lunch, each group having lunch at a different time. A computer randomly assigns each student to one of the four lunch groups. The probability that four friends, Al, Bob, Carol, and Dan, will be assigned to the same lunch group is approximately what?
A) $\frac{1}{256}$
B) $\frac{1}{64}$
C) $\frac{1}{16}$
D) $\frac{1}{4}$

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