
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
We denote by  gcd (...) the greatest common divisor of the numbers in (...). (For example, gcd $(4, 6, 8)=2$  and gcd  $(12, 15)=3$ .) Suppose that positive integers  $a, b, c$  satisfy the following four conditions: $\bullet$  gcd  $(a, b, c)=1$ , $\bullet$  gcd  $(a, b + c)>1$ , $\bullet$  gcd  $(b, c + a)>1$ , $\bullet$  gcd  $(c, a + b)>1$ .
a) Is it possible that  $a + b + c = 2015$ ?
b) Determine the minimum possible value that the sum  $a+ b+ c$  can take.

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