
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
Ajay is at point $A$ in Manaus, Brazil, at $3^\circ$ S latitude and $60^\circ$ W longitude. Billy is at point $B$ in Bangkok, Thailand, at $13^\circ$ N latitude and $100^\circ$ E longitude. Assume that Earth is a perfect sphere with radius $R$ and center $C$. Determine the angle at $C$, $\angle ACB$.

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