
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 $f(x)= \frac{3-x^{2}}{1+x^{2}}$.
(1) Compute the values of $f(3)$, $f(4)$, $f(\frac{1}{3})$ and $f(\frac{1}{4})$;
(2) Conjecture a general conclusion based on the results from (1) and provide a proof;
(3) Evaluate: $f(1)+f(2)+…+f(2015)+f(\frac{1}{2})+f(\frac{1}{3})+…+f(\frac{1}{2015})$

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