
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 $n>1$ be a natural number. Write the fractions $\frac{1}{n}, \frac{2}{n}, \ldots, \frac{n-1}{n}$ and reduce each to its simplest form; denote the sum of the numerators of the resulting fractions by $f(n)$. For which natural numbers $n>1$ do the numbers $f(n)$ and $f(2015n)$ have different parities?

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