
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]


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Given distinct real numbers \(a_{1}, a_{2}, a_{3}\) and \(b\). It turns out that the equation \((x-a_{1})(x-a_{2})(x-a_{3}) = b\) has three distinct real roots \(c_{1}, c_{2}, c_{3}\). Find the roots of the equation \((x+c_{1})(x+c_{2})(x+c_{3}) = b\).

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