
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 school decided to purchase 8 soccer balls and 14 basketballs for $1600 in order to better promote ball sports. It is known that the price of a basketball is $20 more than the price of a soccer ball. Please answer the following questions:<br/>$(1)$ Find the prices of a soccer ball and a basketball;<br/>$(2)$ If the school wants to spend no more than $3240 and at least $3200 to purchase 50 balls, what are the possible purchasing schemes?

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