
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 natural numbers are written in sequence, in increasing order, and by this we get an infinite sequence of digits. Find the least natural  $k$ , for which among the first  $k$  digits of this sequence, any two nonzero digits have been written a different number of times.
 
*Aleksandar Ivanov, Emil Kolev*

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