
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
A convenience store in the neighborhood purchased a certain number of boxes of pure milk and yogurt for $2000$ yuan and $4800$ yuan respectively. It is known that the quantity of yogurt purchased this time is $1.5$ times the quantity of pure milk, and the price of each box of yogurt is $30$ yuan more expensive than each box of pure milk.<br/>$(1)$ Find the quantity of pure milk purchased this time.<br/>$(2)$ During the sales process, each box of pure milk is sold for $80$ yuan and quickly sold out; each box of yogurt is sold at a 25% markup from the purchase price. After selling a portion, just before the May Day holiday, the mall decided to offer a 10% discount on the remaining yogurt. It is known that after selling all the pure milk and yogurt, a total profit of $2150$ yuan was made. Find the number of boxes of yogurt sold at a 10% discount.

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