
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
Define \( f(x) = \frac{x^2}{1 + x^2} \) and suppose that

\[ 
A = f(1) + f(2) + f(3) + \cdots + f(2015) 
\]

\[ 
B = f(1) + f\left(\frac{1}{2}\right) + f\left(\frac{1}{3}\right) + \cdots + f\left(\frac{1}{2015}\right)
\]

(Each sum contains 2015 terms.) Determine the value of \( A + B \).

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