
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 edges of  $K_{2017}$  are each labeled with  $1,2,$  or  $3$  such that any triangle has sum of labels at least  $5.$  Determine the minimum possible average of all  $\dbinom{2017}{2}$  labels.
 
(Here  $K_{2017}$  is defined as the complete graph on 2017 vertices, with an edge between every pair of vertices.)
 
*Proposed by Michael Ma*


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