
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
The function \( f \) satisfies the equation \((x-1) f(x) + f\left(\frac{1}{x}\right) = \frac{1}{x-1}\) for each value of \( x \) not equal to 0 and 1. Find \( f\left(\frac{2016}{2017}\right) \).

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