
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
Given real numbers $x_{1}, x_{2}, \ldots, x_{n} (n \in \mathbb{N}^{*} \text{ and } n \geqslant 2)$ satisfying $|x_{i}| \leqslant 1 (i=1,2,\ldots,n)$, let $S(x_{1},x_{2},\ldots,x_{n})= \sum\limits_{1 \leqslant i < j \leqslant n}x_{i}x_{j}$.  
(Ⅰ) Calculate the values of $S(-1,1,- \frac {2}{3})$ and $S(1,1,-1,-1)$;  
(Ⅱ) When $n=3$, find the minimum value of $S(x_{1},x_{2},x_{3})$;  
(Ⅲ) When $n$ is odd, find the minimum value of $S(x_{1},x_{2},\ldots,x_{n})$.  
Note: $\sum\limits_{1 \leqslant i < j \leqslant n}x_{i}x_{j}$ represents the sum of the products of any two numbers $x_{i}, x_{j} (1 \leqslant i < j \leqslant n)$ among $x_{1}, x_{2}, \ldots, x_{n}$.

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