
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
Eight distinct positive integers are chosen randomly from the numbers $1$ to $3000$. What is the probability that some pair of these integers has a difference that is a multiple of $7$?
A) $ \frac{1}{2} $
B) $ \frac{5}{7} $
C) $ \frac{6}{7} $
D) $ \frac{7}{8} $
E) $ 1 $

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