
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
For what smallest natural number \( n \) can the numbers from 1 to \( n \) be arranged in a circle such that each number is either greater than all of the 40 numbers following it in the clockwise direction or smaller than all of the 30 numbers following it in the clockwise direction?

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