
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
A father wants to distribute his estate to his children: first giving 1000 yuan and $\frac{1}{10}$ of the remaining estate to the eldest child, then 2000 yuan and $\frac{1}{10}$ of the remaining estate to the second child, next 3000 yuan and $\frac{1}{10}$ of the remaining estate to the third child, and so on. It turns out that each child received the same amount of property. How many children does the father have?

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