
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
Let \( A, B, C \) represent the angles of a triangle in radians. Evaluate the determinant
\[
\begin{vmatrix} 
e^{A} & e^{-A} & 1 \\ 
e^{B} & e^{-B} & 1 \\ 
e^{C} & e^{-C} & 1 
\end{vmatrix}.
\]

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