
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
Find the least possible value for the fraction  $$ \frac{lcm(a,b)+lcm(b,c)+lcm(c,a)}{gcd(a,b)+gcd(b,c)+gcd(c,a)} $$  over all distinct positive integers  $a, b, c$ . 
By  $lcm(x, y)$  we mean the least common multiple of  $x, y$  and by  $gcd(x, y)$  we mean the greatest common divisor of  $x, y$ .

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