
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
A list of numbers is created using the following rules:
- The first number is 3 and the second number is 4.
- Each number after the second is the result of adding 1 to the previous number and then dividing by the number before that. In other words, for any three consecutive numbers in the list, \( a, b, c \), we have \( c = \frac{b+1}{a} \).

What is the smallest positive integer \( N \) for which the sum of the first \( N \) numbers in the list is equal to an odd integer that is greater than 2021?

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