
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 increased its lunch groups to four for its 800 students, keeping the size of each group equal. A computer randomly assigns each student into one of these four lunch groups. Calculate the probability that three friends, Dave, Eva, and Frank, will all be assigned to the same lunch group.

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