
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 machine that transforms a positive integer N based on the rule: if N = 7, the machine outputs 3 × 7 + 1 = 22, find the sum of all positive integers N whereby six iterations of the process result in the final output being 1.

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