
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
In a hat box, there are 21 hats and 18 caps. They are to be distributed onto two shelves: the first shelf should hold 20 items, and the second shelf should hold 19 items. After distribution, the percentage of hats on each shelf is calculated, and the resulting numbers are added together. How should the hats be distributed on the shelves to maximize the resulting sum?

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