
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 new machine processes a number $N$ using the following rules: if $N$ is even, it outputs $N + 5$; if $N$ is odd, it outputs $2N$. Suppose the output is fed back to the machine sequentially. Starting from $N=9$, it takes exactly four iterations to get the output $54$. What is the sum of all such starting integers $N$ that result in $54$ in exactly four iterations using the given machine rules?
**A)** 6
**B)** 11
**C)** 22
**D)** 27
**E)** 39

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