
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
During the 2022 Winter Olympics, the mascot Bing Dwen Dwen became popular overnight worldwide, and various Bing Dwen Dwen dolls, pendants, and decorations emerged. A certain school decided to purchase two types of Bing Dwen Dwen ornaments, denoted as type $A$ and type $B$, as souvenirs. It is known that type $A$ costs $25$ yuan more per item than type $B$, and the budget is $1700$ yuan. $800$ yuan is allocated to purchase type $A$ ornaments, and the remaining funds are used to purchase type $B$ ornaments. The quantity of type $B$ ornaments purchased is three times the quantity of type $A$ ornaments. Find the unit prices of type $A$ and type $B$ ornaments.

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