
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 natural number is called good if all its digits are non-zero. A good number is called special if it has at least \( k \) digits and the digits are in strict ascending order from left to right.

Consider a good number. In one move, you are allowed to append a special number to either end or insert it between any two digits of the good number, or, conversely, erase a special number from its representation. For what maximum value of \( k \) can any good number be transformed into any other good number using such moves?

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