
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
**Six distinct positive integers are randomly chosen between $1$ and $5000$, inclusive. What is the probability that some pair of these integers has a difference that is a multiple of $7$?**
A) $\frac{1}{2}$
B) $\frac{3}{5}$
C) $\frac{2}{3}$
D) $\frac{4}{5}$
E) $1$

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