
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 $B$ on the sea, which are $10$ nautical miles apart. When looking from island $A$ to another island $C$ and island $B$, the angle is $60^{\circ}$, and when looking from island $B$ to island $C$ and island $A$, the angle is $75^{\circ}$. Calculate the distance between islands $B$ and $C$.

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