
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 be a natural number  $ n\ge 2 $  and an expression of  $ n $  variables  $$  E\left( x_1,x_2,...,x_n\right) =x_1^2+x_2^2+\cdots +x_n^2-x_1x_2-x_2x_3-\cdots -x_{n-1}x_n -x_nx_1.  $$  Determine  $ \sup_{x_1,...,x_n\in [0,1]} E\left( x_1,x_2,...,x_n\right)  $  and the specific values at which this supremum is attained.

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