
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 new game, 50 participants, including Dean, sit in a circle each holding a calculator. The first calculator reads 2, the second 1, and the third 0. Dean begins by cubing the value on the first calculator, squaring the value on the second calculator, and adding 1 to the value on the third calculator. After performing these operations, he passes the calculators to the next person. Each participant, in turn, applies the same operations to whatever values they receive and then passes the calculators on. Once all calculators have made one complete round back to Dean, what is the sum of the numbers displayed on the calculators?

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