
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
On a driving tour, Adam, Betty, Carol, and Dave were trying to determine how close they were to the nearest gas station. Adam remarked, "We are at least 10 miles away from the gas station," while Betty believed, "We are no more than 7 miles away from it." Carol added, "The gas station is within 5 miles," and Dave claimed, "It can’t be more than 9 miles." Later, it was confirmed that none of these statements were true. Let \( x \) denote the distance in miles to the nearest gas station. What are the possible values of \( x \)?
A) \((7, 10)\)
B) \((7, \infty)\)
C) \((5, 7)\)
D) \((9, \infty)\)
E) \((9, 10)\)

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