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

(1) Calculate the values of $f(2)+f\left(\frac{1}{2}\right)$, $f(3)+f\left(\frac{1}{3}\right)$, and $f(4)+f\left(\frac{1}{4}\right)$ respectively;

(2) Induct a general conclusion and provide a proof;

(3) Calculate the value of $f(1)+f(2)+f(3)+…+f(2017)-\left(f\left(\frac{1}{2}\right)+f\left(\frac{1}{3}\right)+……+f\left(\frac{1}{2017}\right)\right)$

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