
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
Sasha discovered that there are exactly \( n \) working buttons with digits on the calculator. It turned out that any natural number from 1 to 99,999,999 can either be entered using only the working buttons or obtained as the sum of two natural numbers, each of which can be entered using only the working buttons. What is the smallest \( n \) for which this is possible?

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