
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
Master Wang went to the fruit wholesale market to purchase apples. He was interested in the apples from two stores, $A$ and $B$, which have the same quality of apples. The retail price of the apples in both stores is $6$ yuan per kilogram, but the wholesale prices are different. Store $A$ has the following rules:
- For a one-time wholesale quantity not exceeding $1000$ kilograms, a discount of $92\%$ off the retail price is applied.
- For a one-time wholesale quantity exceeding $1000$ kilograms but not exceeding $2000$ kilograms, a discount of $90\%$ off the retail price is applied.
- For a one-time wholesale quantity exceeding $2000$ kilograms, a discount of $88\%$ off the retail price is applied.

Store $B$ has segmented pricing as shown in the table below:

| Quantity Range (kg) | $0\sim 500$ | $500$ above $\sim 1500$ | $1500$ above $\sim 2500$ | $2500$ above |
|---------------------|-------------|------------------------|-------------------------|-------------|
| Price               | $95\%$      | $85\%$                 | $75\%$                  | $70\%$      |

$(1)$ If he plans to wholesale $800$ kilograms of apples, which store offers a better deal?
$(2)$ If he only wholesales $x$ kilograms of apples from one store $\left(1500 \lt x \lt 2000\right)$, calculate the cost for him to wholesale from stores $A$ and $B$ (express the cost as an algebraic expression involving $x$ and simplify).

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