
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 real solutions of the equation

$$
\begin{aligned}
& \sqrt{a+b x}+\sqrt{b+c x}+\sqrt{c+a x}= \\
& =\sqrt{b-a x}+\sqrt{c-b x}+\sqrt{a-c x}
\end{aligned}
$$

given that it has solutions.

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