
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
In a certain sea area, there are three islands A, B, and C. It is known that the distance between A and B is 8n miles, and the distance between A and C is 5n miles. The angle ∠BAC measured from island A is 60°. What is the distance between island B and C in n miles?

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