
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
In a game with 50 participants sitting in a circle, each holding one calculator, three calculators among them are set to 1, 0, and -1 respectively. Each participant performs specific operations on the calculators: the one showing 1 is cubed, the one showing 0 is squared, and the one showing -1 is negated. After performing these operations, each participant passes the calculators to the next person in the circle. This continues until each calculator has been passed around the entire circle. When all calculators have returned to their starting points, the numbers displayed are added together. What is the sum of the numbers on the calculators?

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