
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
From the peak of a mountain $(C)$, two objects $(A$ and $B)$ are visible on the seashore, which are $15 \mathrm{~km}$ apart. The angle subtended by the distance $A B$ is $60^{\circ}$, the angle of depression to $A$ is $10^{\circ}$, and to $B$ is $12^{\circ}$. What is the height of the mountain?

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