
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 the function \( f: \mathbb{Z} \rightarrow \mathbb{Z} \) take only integer inputs and have integer outputs. For any integers \( x \) and \( y \), \( f \) satisfies
\[ f(x) + f(y) = f(x+1) + f(y-1) \]

If \( f(2016) = 6102 \) and \( f(6102) = 2016 \), what is \( f(1) ?\)

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