
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
Given a positive integer N, calculate the output of the machine after applying the 6-step process N → 3N + 1 → 3M + 1 → 3K + 1 → 3J + 1 → 3I + 1 → 1, where M = N, K, J, I, and the sum of all such integers N.

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