
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 value of $f(2)+f(\frac{1}{2})$ and $f(3)+f(\frac{1}{3})$;
(2) Make a conjecture about the value of $f(x)+f(\frac{1}{x})$ (without proof);
(3) Find the value of $f(2)+f(3)+f(4)+...+f(2016)+f(\frac{1}{2016})+...+f(\frac{1}{4})+f(\frac{1}{3})+f(\frac{1}{2})$.

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