
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
Let's call those natural numbers slightly unlucky where the sum of their digits in the decimal system is divisible by 13. What is the maximum difference between consecutive slightly unlucky numbers?

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