
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 version of the game, 44 participants (including Dean) sit in a circle. Dean holds three calculators showing numbers 2, 0, and -2, respectively. Dean starts by pressing the square root button on the calculator showing 2, the square button on the one showing 0, and the factorial button (considered for non-negative integers only) on the calculator that shows -2 (assume factorial of negative integers are undefined and remain unchanged). Each participant repeats the same operations on their turn before passing the calculators to the next person. What is the sum of the numbers on the calculators when they return to Dean?

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