
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
For each positive integer \( n \), let \( g(n) \) be the greatest common divisor (GCD) of \( n \) and 2015. Find the number of ordered triplets \((a, b, c)\) that satisfy the following conditions:
1. \( a, b, c \in \{1, 2, \cdots, 2015\} \);
2. The seven numbers \( g(a), g(b), g(c), g(a+b), g(b+c), g(c+a), g(a+b+c) \) are all distinct.

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