
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 $f(2)+f( \frac{1}{2})$, $f(3)+f( \frac{1}{3})$, $f(4)+f( \frac{1}{4})$, and conjecture a general conclusion (proof is not required);
(2) Calculate the value of $2f(2)+2f(3)+…+2f(2017)+f( \frac{1}{2})+f( \frac{1}{3})+…f( \frac{1}{2017})+ \frac{1}{2^{2}}f(2)+ \frac{1}{3^{2}}f(3)+…+ \frac{1}{2017^{2}}\cdot f(2017)$.

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