
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's soccer team needs to purchase soccer balls from two brands, $A$ and $B$. It is known that the unit price of brand $A$ soccer balls is $20$ yuan higher than the unit price of brand $B$ soccer balls. It is also known that the quantity of brand $A$ soccer balls that can be purchased with $900$ yuan is equal to the quantity of brand $B$ soccer balls that can be purchased with $720$ yuan.
$(1)$ Find the unit prices of brand $A$ and brand $B$ soccer balls.
$(2)$ If the soccer team plans to purchase a total of $90$ soccer balls from brand $A$ and brand $B, with the quantity of brand $A$ soccer balls being no less than $63$, and the total cost of purchasing both brands of soccer balls not exceeding $8500$ yuan. Let $m$ be the quantity of brand $A$ soccer balls purchased, and the total cost be $W$ yuan. How many purchasing plans does the team have? Which purchasing plan will result in the lowest total cost? What is the lowest total cost?

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