
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
During a camping trip, Emily, Felipe, George, and Hannah are debating how far they are from the nearest village. Emily claims, "We are at least 8 miles away," Felipe argues, "The village is at most 7 miles away," George adds, "We cannot be further than 6 miles from the village," and finally, Hannah concludes, "We are at least 10 miles away from the village." It turns out all their statements are false. Let \( d \) be the distance in miles to the nearest village. Which of the following intervals is the set of all possible values of \( d \)?
A) $(6,7)$
B) $(7,8)$
C) $(6,8)$
D) $(7,10)$
E) $(8,10)$

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