
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
Dean participates in a game with 50 friends (51 people total), each holding one of three calculators showing 2, 0, and -2 respectively. Dean starts with the calculator showing 2 and doubles it, with the calculator showing 0 he squares it, and with the calculator showing -2, he negates it. After performing these operations, he passes them to the next person, who repeats the same operations. After the calculators have gone around the circle so that everyone has had one turn, Dean adds up the numbers on the calculators. What is the sum he ends up with?

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