
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
 $2014$  points are placed on a circumference. On each of the segments with end points on two of the  $2014$  points is written a non-negative real number. For any convex polygon with vertices on some of the  $2014$  points, the sum of the numbers written on their sides is less or equal than  $1$ . Find the maximum possible value for the sum of all the written numbers.

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