
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
Someone, upon dying, left a will according to which the eldest son receives 100 francs and one-tenth of the remainder, the second son receives 200 francs and one-tenth of the new remainder, the third son receives 300 francs and one-tenth of the new remainder, and so on until the last son. The shares of all sons should be equal. Find the size of the inheritance left, the number of sons, and each son's share.

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