
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
Find all values of the parameters \(a, b, c\) for which the system of equations
\[
\left\{
\begin{array}{l}
a x + b y = c \\
b x + c y = a \\
c x + a y = b
\end{array}
\right\}
\]
has at least one negative solution (where \(x, y < 0\)).

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