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

(2) Find the value of $\left[2f(2)+2f(3)+⋯+2f(2018)\right]+\left[f( \frac{1}{2})+f( \frac{1}{3})+⋯+f( \frac{1}{2018})\right]+\left[ \frac{1}{2^{2}}f(2)+ \frac{1}{3^{2}}f(3)+⋯+ \frac{1}{2018^{2}}f(2018)\right]$

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