
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 while ago, a certain middle school went to the "Li Ning Sports Supplies" store to purchase a batch of basketballs and soccer balls for the construction of the school gym. It is known that 2 soccer balls and 3 basketballs cost a total of $410, and 5 soccer balls and 2 basketballs cost a total of $530.  
$(1)$ What is the price of each basketball and soccer ball?  
$(2)$ Now, the "Li Ning Sports Supplies" store is conducting a promotion, offering the same discount on all products. Currently, purchasing 5 soccer balls and 5 basketballs only costs $680. What is the discount rate at which the store is selling the items based on the original price?

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