
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
When an integer $N$ is put into a machine, it produces the number according to the following rule:
- If $N$ is odd, the output $O = 3N + 4$.
- If $N$ is even, $O = \frac{N}{2}$.

If an input $N$ is processed four times by this machine, and the final output is $5$, what is the sum of all possible initial integers $N$?
\[ N \to \rule{0.5cm}{0.15mm} \to \rule{0.5cm}{0.15mm} \to \rule{0.5cm}{0.15mm} \to 5 \]
**A)** $60$
**B)** $80$
**C)** $100$
**D)** $120$
**E)** $150$

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