
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
Let \( f \) and \( g \) be functions such that for all real numbers \( x \) and \( y \),
\[ g(f(x+y)) = f(x) + (x+y)g(y). \]

Find the value of \( g(0) + g(1) + \cdots + g(2013) \).

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