
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

Tanya sequentially wrote out numbers of the form $\{\lfloor n \wedge 7 - 1 \rfloor\}$ for natural numbers $n = 2, 3,$ and so on, and noticed that for $n = 8$, the number obtained is divisible by 337. What is the smallest $n > 1$ for which she will obtain a number divisible by 2022?

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