
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 \( f(x) \) be a function defined on the set of integers such that:
1. \( f(1) = 1 \), \( f(2) = 0 \)
2. For any \( x \) and \( y \), the following holds:
   \[
   f(x+y) = f(x) f(1-y) + f(1-x) f(y)
   \]

Find \( f(2015) \).

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