
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
An input $N$ into a machine results in output $O$ according to the rule: if $N$ is odd, $O = 3N + 1$, if $N$ is even, $O = \frac{N}{2}$. After repeatedly inputting the output back into the machine for a total of seven steps starting from $N$, the final output is $10$. Find the sum of all possible starting integers $N$ that lead to this outcome.
A) 1270
B) 2540
C) 5100
D) 10200

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