
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
In order to implement General Secretary Xi's important instructions on "double reduction" work and enhance students' physical fitness, a certain middle school in Jinan city decided to purchase some basketballs and soccer balls to promote students' physical exercise. It is known that the unit price of each basketball is $20$ yuan more than the unit price of each soccer ball, and the cost of purchasing basketballs for $6000$ yuan is $1.25$ times the cost of purchasing soccer balls for $3200$ yuan.

$(1)$ Find the unit prices of basketballs and soccer balls respectively.

$(2)$ According to the actual needs of the school, a total of $200$ basketballs and soccer balls need to be purchased at once, and the total cost of purchasing basketballs and soccer balls should not exceed $9600$ yuan. How many soccer balls should the school purchase at least?

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