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

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