
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
Biot and Gay-Lussac, French natural scientists, ascended in a balloon in 1804 and reached a height of $6825 \mathrm{~m}$. The questions are: How many kilometers did the horizon extend to on this occasion and how many $\mathrm{km}^{2}$ of land area could be overseen from the balloon? (The Earth's radius is $6377.4 \mathrm{~km}$.)

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