
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 a ship sails northward at a velocity of $22\sqrt{6}\text{ km/h}$, and at point A, a lighthouse S is observed at $45^\circ$ northeast of the ship. After $1$ hour and $30$ minutes, the ship reaches point B, where the lighthouse S is observed at $15^\circ$ southeast of the ship, determine the distance between the lighthouse S and point B.

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