
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
Euler was not only a great mathematician but also a father who was good at educating his children. The following problem is one he created to enlighten his children: "Before his death, the father made a will to distribute his estate in the following manner: the eldest son would receive 100 francs plus 1/10 of the remainder; the second son would receive 200 francs plus 1/10 of the remainder; the third son would receive 300 francs plus 1/10 of the remainder; and so on for the other children. In the end, it was found that the estate was completely distributed and all the children received an equal share." How much did each child inherit?

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