
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 \(n\) be a positive integer greater than 1. Consider the fractions \(\frac{1}{n}, \frac{2}{n}, \cdots, \frac{n-1}{n}\) in their simplest forms. Let \(f(n)\) denote the sum of the numerators of these simplest fractions. If \(f(n)\) and \(f(2015 n)\) have different parity (i.e., one is odd and the other is even), find all possible values of \(n\).

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