
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 box, we pack 187 books that weigh a total of \( 189 \mathrm{~kg} \). The average weight of the large-sized books is \( 2.75 \mathrm{~kg} \), the medium-sized ones weigh \( 1.5 \mathrm{~kg} \) on average, and the small-sized ones weigh \( \frac{1}{3} \mathrm{~kg} \) on average. How many books are there of each size if the total weight of the large-sized books is the greatest, while the total weight of the small-sized books is the smallest?

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