
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
Given that \(a\), \(b\), and \(c\) are three non-zero real numbers and \(x^2-1\) is a factor of the polynomial \(x^3 + a x^2 + b x + c\), calculate the value of \(\frac{a b + 3 a}{c}\).

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