
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
The polynomial \(x^3 - 2015x^2 + mx + n\) has integer coefficients and three distinct positive zeros. Exactly one of these is an integer, and it is the average of the other two. Determine the number of possible values for \(n\).

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