
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
To implement the spirit of documents such as the "Healthy China Action (2019-2030)", a certain school is preparing to purchase a batch of soccer balls and volleyballs to promote campus sports activities. It is known that the price of each soccer ball at a certain sports equipment supermarket is $20$ yuan more than the price of a volleyball. The number of soccer balls purchased with $500$ yuan is equal to the number of volleyballs purchased with $400$ yuan.  
$(1)$ Find the price of each soccer ball and volleyball.  
$(2)$ The school decides to purchase a total of $50$ soccer balls and volleyballs, with the number of soccer balls purchased not less than the number of volleyballs. Find the minimum amount of money spent on this purchase.

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