
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
The product $M$ of three positive integers is $8$ times their sum, and one of the integers is the sum of the other two. Additionally, one of the integers is twice another. Find the sum of all possible values of $M$.

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