
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 famous Swiss mathematician Euler once posed the following problem: A father made a will before his death, distributing his inheritance in the following way: the eldest child received 100 Swiss francs and $\frac{1}{10}$ of the remaining amount; the second child received 200 Swiss francs and $\frac{1}{10}$ of the remaining amount; the third child received 300 Swiss francs and $\frac{1}{10}$ of the remaining amount, and so on, giving the rest to the remaining children. It was found that after the entire inheritance was distributed, all the children received an equal amount. What was the total amount of the father's inheritance in Swiss francs?

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