
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 pairs of real numbers  $a, b$  for which the equation in the domain of the real numbers
\[\frac{ax^2-24x+b}{x^2-1}=x\]
has two solutions and the sum of them equals  $12$ .

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