
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
Given the sequence defined by $O = \begin{cases} 3N + 2, & \text{if } N \text{ is odd} \\ \frac{N}{2}, & \text{if } N \text{ is even} \end{cases}$, for a given integer $N$, find the sum of all integers that, after being inputted repeatedly for 7 more times, ultimately result in 4.

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