
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 down numbers of the form \( n^{7} - 1 \) for natural numbers \( n = 2, 3, \ldots \) and noticed that for \( n = 8 \), the resulting number is divisible by 337. For what smallest \( n > 1 \) will she get a number divisible by 2022?

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