
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
In an infinite increasing sequence of natural numbers, each number is divisible by at least one of the numbers 1005 and 1006, but none is divisible by 97. Additionally, any two consecutive numbers differ by no more than $k$. What is the smallest possible $k$ for this scenario?

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