
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
Given that islands $A$ and $B$ are $10n$ miles apart, the angle of view from island $A$ to island $B$ and island $C$ is $60^{\circ}$, and the angle of view from island $B$ to island $A$ and island $C$ is $75^{\circ}$. Determine the distance between islands $B$ and $C$ in $n$ miles.

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