
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 a positive integer $N$ is fed into a machine, the output is calculated according to the rule below. For example, if the input is $N=8$, the output is $4 \cdot 8 + 2 = 34$. When this output is repeatedly inserted into the machine seven more times, the final output is $50$.
\[8 \to 34 \to 17 \to 70 \to 35 \to 142 \to 71 \to 286 \to 50\]
Find the sum of all such integers $N$ where, after applying the same 8-step process, the final output is $2$.
\[N \to \cdots \to 2\]
A) 930
B) 960
C) 980
D) 1000
E) 1020

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