
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 machine transforms a positive integer \( N \) using the following rule: when \( N \) is odd, the output is \( 3N + 1 \); when \( N \) is even, the output is \( \frac{N}{2} \). Starting from an input of \( N = 13 \), the machine outputs \( 3 \cdot 13 + 1 = 40 \). If the output is repeatedly inserted into the machine four more times, the final output is \( 10 \). 
\[ 13 \to 40 \to 20 \to 10 \to 5 \to 16 \to 8 \]
When the same 6-step process is applied to a different starting value of \( N \), the final output is \( 8 \). Find the sum of all such integers \( N \).
A) 960
B) 1000
C) 1016
D) 1024
E) 1048

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