
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 great-grandfather banker left an inheritance to his newborn great-grandson. According to the bank agreement, the amount in the great-grandson's account increases. Each year, on the day after his birthday, the current amount increases by one million rubles more than the previous year. Thus, if the initial amount was zero rubles, after one year it will be +1 million rubles; after 2 years, $1+2$ million rubles; after 3 years, $1+2+3$; and so on. According to the agreement, the process will stop, and the great-grandson will receive the money when the amount in the account is a three-digit number consisting of three identical digits.

How old will the great-grandson be when the conditions of the agreement are fulfilled?

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