
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 real numbers $a \neq b$ and satisfying $a^{2}-8a+5=0$, $b^{2}-8b+5=0$, calculate the value of the algebraic expression $\frac{b-1}{a-1}+\frac{a-1}{b-1}$.

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