
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
A lotto set contains 90 barrels, numbered with natural numbers from 1 to 90. The barrels are somehow distributed among several bags (each bag containing more than one barrel). We'll call a bag good if the number of one of its barrels is equal to the product of the numbers of the remaining barrels in the same bag (for example, the bag "$2,3,6$" is good, while "$4,5,10$" is not). What is the maximum possible number of good bags?

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