
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

Let's call a triplet of numbers chosen from the set {1, 2, 3, 4, 5} good if no two numbers from this triplet sum to 6. Silvia multiplied all the numbers in each good triplet and then added all the resulting products. What number did she get as a result?

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