
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 separated by a distance of $10 \sqrt {2}n$ miles on the sea. The angle of sight from island A to island C and to island B is 60°, and the angle from island B to island C and to island A is 75°. Find the distance between island B and island C, denoted as BC (in miles).

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