
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 property among his children: first giving 1000 yuan and $\frac{1}{10}$ of the remaining property to the eldest child, then giving 2000 yuan and $\frac{1}{10}$ of the remaining property to the second child, and then giving 3000 yuan and $\frac{1}{10}$ of the remaining property to the third child, and so on. It turns out that each child receives the same amount of property. The father has $\qquad$ children.

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