
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
On a circle, 2009 numbers are placed, each of which is equal to 1 or -1. Not all numbers are the same. Consider all possible groups of ten consecutive numbers. Find the product of the numbers in each group of ten and sum them up. What is the largest possible sum?

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