
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 ship $A$ is located at $80^{\circ}$ north by east of lighthouse $C$, and the distance from ship $A$ to lighthouse $C$ is $2\,km$, and ship $B$ is located at $40^{\circ}$ north by west of lighthouse $C$, and the distance between ships $A$ and $B$ is $3\,km$, determine the distance from ship $B$ to lighthouse $C$.

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