
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 processes a positive integer \( N \) according to the following modified rule:

- If \( N \) is odd, the output \( O = 2N + 2 \).
- If \( N \) is even, the output \( O = \frac{N}{2} + 1 \).

When the same 6-step process is applied with a starting value of \( N \), the final output is \( 5 \). What is the sum of all such integers \( N \) that lead to \( 5 \) as the final output after six applications of the machine's rules?
A) 34
B) 66
C) 70
D) 82
E) 83

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