
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
If the function $f(x)= \frac{x^{2}-1}{x^{2}+1}$, then

$(1) \frac{f(2)}{f\left(\frac{1}{2}\right)}=$\_\_\_\_\_\_\_\_; 

$(2) f(3)+f(4)+\ldots+f(2017)+f\left(\frac{1}{3}\right)+f\left(\frac{1}{4}\right)+\ldots+f\left(\frac{1}{2017}\right)=$\_\_\_\_\_\_\_\_.

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