
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   $n\ge 2$  is a given integer ,  $x_1,x_2,\ldots,x_n $  be real numbers such that  $(1) x_1+x_2+\ldots+x_n=0 $ , $(2) |x_i|\le 1$   $(i=1,2,\cdots,n)$ .
Find the maximum of Min $\{|x_1-x_2|,|x_2-x_3|,\cdots,|x_{n-1}-x_n|\}$ .

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