
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
The ancient Indian mathematician Bhaskara mentioned the following problem in his book "Lilavati": "A person distributes money to several people, giving 3 dollars to the first person, 4 dollars to the second person, 5 dollars to the third person, and so on, increasing the amount given by 1 dollar for each subsequent person. After distributing all the money, he collects it back and then redistributes it so that each person gets exactly 100 dollars. How many people are there in total?"

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