
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 toy store purchased a batch of children's toys for $2500$ yuan. After they were put on the market, they quickly sold out. Then, they purchased a second batch of the same toys for $4500$ yuan. The quantity purchased in the second batch was $1.5$ times that of the first batch, but the cost per set increased by $10$ yuan.<br/>$(1)$ Find the cost per set of the toys in the first batch.<br/>$(2)$ If the selling price per set of the two batches of toys is the same, and after selling all the toys, the store wants to make a profit of at least $1750$ yuan, what is the minimum selling price per set?

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