
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 arranged in a circle, each being 1 or -1, and not all numbers are the same. Consider the sums of all products of 10 consecutive numbers.

a) What is the smallest possible sum?

b) What is the largest possible sum?

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