
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 field trip, three students estimated the height of a mountain they were about to climb. Peter said, "The mountain is at least 8000 feet high." Mary said, "It is at most 7900 feet high." John claimed, "Actually, the mountain is at most 7500 feet high." However, none of the statements turned out to be true. Let $h$ be the height in feet of the mountain. Which interval correctly represents all possible values of $h$?
A) $(7500,7900)$
B) $(7900,8000)$
C) $(7500,8000)$
D) $(7900,\infty)$

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