
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  $g(n)$  be the greatest common divisor of  $n$  and  $2015$ . Find the number of triples  $(a,b,c)$  which satisfies the following two conditions: $1)$   $a,b,c \in$  { $1,2,...,2015$ }; $2)$   $g(a),g(b),g(c),g(a+b),g(b+c),g(c+a),g(a+b+c)$  are pairwise distinct.

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