
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
Alice, Bob, and Charlie were on a hike and were pondering how far away the nearest river was. Alice remarked, "We are at least 8 miles away," Bob noted, "We are at most 7 miles away," and Charlie mentioned, "Actually, the nearest river is at most 6 miles away." It turned out that none of the three statements were true. Let \( d \) be the distance in miles to the nearest river. What is the set of all possible values of \( d \)?
**A)** \( (6,7) \)  
**B)** \( (6,8) \)  
**C)** \( (7,8) \)  
**D)** \( (7,\infty) \)  
**E)** \( (5,7) \)

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