
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 continuous function defined on the interval \([0, 2015]\), and \( f(0) = f(2015) \). Find the minimum number of real number pairs \((x, y)\) that satisfy the following conditions:
1. \( f(x) = f(y) \);
2. \( x - y \in \mathbf{Z}_{+} \).

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