
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 certain fruit shop purchased a batch of fruits for $1100$ yuan, which was well received by consumers. Therefore, they purchased a second batch for $1100$ yuan. Since the price of the second batch was increased by $10\%$ based on the first batch, the quantity purchased was $2$ kilograms less than the first batch.<br/>$(1)$ Find the purchase price of the first and second batches of fruits;<br/>$(2)$ During the sales process, the fruit shop sold $\frac{3}{5}$ of the first and second batches of fruits at a price of $80$ yuan per kilogram. In order to sell the remaining fruits quickly, they decided to reduce the price. If the total profit from the two batches of fruits is not less than $1000$ yuan, find the minimum selling price per kilogram of the fruits after the price reduction.

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