
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 $f\left( x \right)=\frac{{{x}^{2}}}{1+{{x}^{2}}}$.

(1) Find the values of $f\left( 2 \right)+f\left( \frac{1}{2} \right),f\left( 3 \right)+f\left( \frac{1}{3} \right),f\left( 4 \right)+f\left( \frac{1}{4} \right)$ and conjecture a general conclusion (proof is not required);

(2) Evaluate: $2f(2)+2f(3)+⋯+2f(2017)+f( \frac{1}{2})+f( \frac{1}{3})+⋯+f( \frac{1}{2017})+ \frac{1}{{2}^{2}}f(2)+ \frac{1}{{3}^{2}}f(3)+⋯+ \frac{1}{{2017}^{2}}f(2017)$.

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