
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 triplet of real numbers \( A, B, C \) is such that \( \sin A + \sin B + \sin C = 0 \) and \( \cos A + \cos B + \cos C = 0 \). Find the value of the expression

\[
\cos(A - B) + \cos(B - C) + \cos(C - A).
\]

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