
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
Meteorological data indicates that for every increase in height of $100$ meters, the temperature drops by approximately $0.6^{\circ}\mathrm{C}$.

(1) The Tian Du Peak of Huangshan in China has an approximate height of $1800$ meters. When the temperature at the foot of the mountain is $18^{\circ}\mathrm{C}$, find the temperature at the mountain top.

(2) Two researchers, in order to estimate the height of a certain mountain peak, measured the temperatures at the foot and the top of the mountain at $10$ AM as $10^{\circ}\mathrm{C}$ and $-8^{\circ}\mathrm{C}$ respectively. Can you help them calculate the height of this mountain peak?

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