
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 Chinese mathematical classic "Zhang Qiu Jian Suan Jing" presents the following "Money Distribution Problem": "There are some people to be given money. The first person is given three coins, the second person four coins, the third person five coins, and so on, with each subsequent person receiving one more coin than the previous person. When the distribution is complete, the money is pooled together and redistributed evenly so that each person receives one hundred coins. How many people are there?" The number of people in the "Money Distribution Problem" is ______.

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