
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
During the Double Eleven shopping festival, Bai Bai and his mother went to the mall together and found that two malls sold the same items at the same price, but the discount schemes offered by the two malls were different. In Mall A, after accumulating purchases exceeding $200, the excess amount is discounted at 15% off the original price. In Mall B, after accumulating purchases exceeding $100, the excess amount is discounted at 10% off the original price.  
$(1)$ When the total shopping amount is $300$, which mall is more cost-effective to shop at? Why?  
$(2)$ At what amount of shopping (greater than $100$) will the cost be the same at both Mall A and Mall B?

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