
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
Let  $S$  be a randomly selected four-element subset of  $\{1, 2, 3, 4, 5, 6, 7, 8\}$ . Let  $m$  and  $n$  be relatively prime positive integers so that the expected value of the maximum element in  $S$  is  $\dfrac{m}{n}$ . Find  $m + n$ .

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