
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
A ship is sailing north at a speed of $32$ miles per hour. It sees a lighthouse at point $(A)$ in the northeast direction at an angle of ${30^{0}}$. After half an hour, the ship sails to point $(B)$ and sees the lighthouse in the northeast direction at an angle of ${75^{0}}$. Calculate the distance between the lighthouse and point $(B)$ in miles.

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