
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
All four-digit numbers from 1000 to 9999 are written consecutively without spaces. Kostya underlined $k$ digits in a row in this sequence, and Andrey underlined another $k$ digits in a row in this sequence. It turned out that the $k$-digit numbers underlined by the boys were equal. What is the largest possible $k$ for which this could happen?

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