
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
a) Each of the numbers  $x_1,x_2,...,x_n$  can be  $1, 0$ , or  $-1$ . 
What is the minimal possible value of the sum of all products of couples of those numbers. 
b) Each absolute value of the numbers  $x_1,x_2,...,x_n$   doesn't exceed  $1$ . 
What is the minimal possible value of the sum of all products of couples of those numbers.

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