
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 decimal representation of a natural number \( N \) consists only of the digits 1 and 2. It is known that by removing digits from this number, any of the 10,000 numbers consisting of 9999 ones and one two can be obtained. Find the smallest possible number of digits in the representation of \( N \).

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