
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
109 books were purchased for gifting 109 people at a total cost of $2845 \mathrm{Ft}$. It happened that the prices of the books were limited to just three values: $34 \mathrm{Ft}$, $27.50 \mathrm{Ft}$, and $17.50 \mathrm{Ft}$. Determine how many books belong to each of the three price categories, knowing that the quantities of books priced the same did not differ significantly.

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