
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 store plans to purchase two different models of tablets, model A and model B, totaling 20 units. It is known that the cost price of model A tablet is 1600 yuan and the selling price is 2000 yuan; the cost price of model B tablet is 2500 yuan and the selling price is 3000 yuan.<br/>$(1)$ If the store purchases $x$ units of model A tablets, please write down the function expression between the profit $y$ and $x$ after all units are sold.<br/>$(2)$ If the total cost of purchasing both types of tablets does not exceed 39200 yuan, and the profit after selling all units is not less than 8500 yuan, please design all purchasing plans, and find the purchasing plan that maximizes the profit and the maximum profit.

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