
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
Supermarkets A and B sell the same goods at the same price. In order to attract customers, they each offer different discount schemes. After purchasing goods exceeding $200$ yuan at supermarket A, the excess amount is discounted at the original price of $20\%$. After purchasing goods exceeding $100$ yuan at supermarket B, the excess amount is discounted at the original price of $15\%$. Let the original cost of shopping for a customer be $x$ yuan $\left(x > 200\right)$.<br/>$(1)$ Li Minghui plans to buy goods worth $300$ yuan. In your opinion, which supermarket should he go to? Please explain your reasoning;<br/>$(2)$ Calculate how much Li Minghui needs to spend on goods so that the cost of shopping at both supermarkets is the same?

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