
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 the ancient Chinese mathematical classic "Zhang Qiu Jian Suan Jing," there is a "money distribution problem": There is money to be distributed among several people. The first person receives 3 coins, the second person receives 4 coins, the third person receives 5 coins, and so on, with each subsequent person receiving one more coin than the previous person. After distributing all the money, it is collected back and then redistributed evenly among all the people, resulting in each person receiving 100 coins. The question is: How many people are there? The number of people in this problem is __________.

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