
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
If  $8/19$  of the product of the two largest elements of a positive integer set is not greater than the sum of the other elements, calculate the minimum possible value of the largest number in the set.

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