
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
Determine the greatest real number  $ C $ , such that for every positive integer  $ n\ge 2 $ , there exists  $ x_1, x_2,..., x_n  \in [-1,1]$ , so that  $$ \prod_{1\le i<j\le n}(x_i-x_j) \ge C^{\frac{n(n-1)}{2}} $$  .

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