
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
Given an adventure team of 8 people, including 3 medical staff, the team is divided into groups A and B, each with 4 people.

(I) Calculate the probability that one of the groups A or B has exactly one medical staff.
(II) Calculate the probability that group A has at least two medical staff.
(III) Calculate the mathematical expectation of the number of medical staff, denoted as ξ, in group A.

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