
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
A, B, and C are hiking and want to know the distance to the nearest town. A says, "At least 6 miles." B says, "At most 5 miles." C says, "At most 4 miles." In fact, all three of them are wrong. Let $d$ represent their distance to the nearest town. Determine the interval to which $d$ belongs.

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