
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
If \(a, b, c\) are nonzero real numbers and satisfy 
\[
\begin{array}{l}
\frac{a+b-c}{c}=\frac{a-b+c}{b}=\frac{-a+b+c}{a}, \\
x=\frac{(a+b)(b+c)(c+a)}{abc}, \quad \text { and } x<0,
\end{array}
\] calculate the value of \(x\).

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