
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 from point $A$ in a direction of $60^{\circ}$ north of east for $30n$ miles to reach island $B$. Then, it sails from $B$ in a direction of $60^{\circ}$ south of east for $50n$ miles to reach island $C$. If the ship sails directly from $A$ to $C$ next time in a direction of $\theta$ south of east, then the value of $\cos \theta$ is __________.

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