
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
20 numbers: \(1, 2, \ldots, 20\) are divided into two groups. It turns out that the sum of the numbers in the first group is equal to the product of the numbers in the second group. a) What is the smallest and b) the largest number of numbers that can be in the second group?

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