
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 sails north at a speed of $24\sqrt{6}km/h$. From point $A$, the lighthouse $S$ is observed to be in the northeast direction at an angle of $45^{\circ}$. After sailing for $1$ hour and $30$ minutes, the ship reaches point $B$, where the lighthouse $S$ is observed to be in the south-east direction at an angle of $75^{\circ}$. What is the distance between the lighthouse $S$ and point $B$?

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