
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
For an integer \( n \geq 0 \), let \( f(n) \) be the smallest possible value of \( |x+y| \), where \( x \) and \( y \) are integers such that \( 3x - 2y = n \). Evaluate \( f(0) + f(1) + f(2) + \cdots + f(2013) \).

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