
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
There are 999 numbers placed on a circle, each equal to either 1 or -1, and not all numbers are the same. Consider all products of 10 consecutive numbers and sum them up.

a) What is the minimum sum that can be obtained?

b) What is the maximum sum that can be obtained?

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