
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
Five students stand in a circle and count in turn, with the following rules: The first student starts with the number 1, the second student starts with the number -2, the third student's number is the difference between the second and the first student's numbers, the fourth student's number is the difference between the third and the second student's numbers, and so on. What is the sum of the first 100 numbers announced?

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