
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
There are two islands, $A$ and $B$, in the sea that are $10\,n\text{ mile}$ apart. The angle formed by looking at island $C$ from island $A$ and island $B$ is $60^{\circ}$, and the angle formed by looking at island $C$ from island $B$ and island $A$ is $75^{\circ}$. What is the distance between island $B$ and island $C$ in $n\text{ mile}$?

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