
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
Suppose there exists a machine where for a positive integer $N$, the rule applied is:
- If $N$ is odd, produce $3N + 4$.
- If $N$ is even, produce $\frac{N}{2}$.

When $N = 9$, and the output is repeatedly fed into the machine six more times, the final output is $5$.

Given:
\[9 \to 31 \to 97 \to ... \to 5\]

Find a $6$-step process when applied to a different starting value of $N$, that yields the final output as $11$. What is the sum of all such integers $N$?
A) 100
B) 352
C) 528
D) 576
E) 704

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