
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
Consider a machine that when a positive integer $N$ is entered, the machine's processing rule is:

- If $N$ is odd, output $4N + 2$.
- If $N$ is even, output $N / 2$.

Using the above rule, if starting with an input of $N = 9$, after following the machine's process for six times the output is $22$. Calculate the sum of all possible integers $N$ such that when $N$ undergoes this 6-step process using the rules above, the final output is $10$.
A) 320
B) 416
C) 540
D) 640
E) 900

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