
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
"Green-heart kiwi" and "Red-heart kiwi" are specialties of Xixia, Nanyang, Henan. Xixia is located at the junction of temperate and subtropical zones. It is the earliest region in China to carry out artificial cultivation of kiwi and also the region with the most wild kiwi resources that can be utilized. The unique climatic conditions of Xixia result in excellent intrinsic quality of the kiwi produced there, not only with good taste but also high in vitamin $C$. A fruit store in Zhengzhou plans to sell "Green-heart kiwi" and "Red-heart kiwi", and decides to sell "Red-heart kiwi" at a price $25$ yuan more expensive per box than "Green-heart kiwi", selling $6$ boxes of "Green-heart kiwi" for a total price $25$ yuan less than selling $5$ boxes of "Red-heart kiwi". (Each box contains $10$ kilograms)<br/>$(1)$ What are the prices per box of "Green-heart kiwi" and "Red-heart kiwi"?<br/>$(2)$ If the cost price per box of "Green-heart kiwi" is $80$ yuan and the cost price per box of "Red-heart kiwi" is $100$ yuan. Now the fruit store plans to purchase a total of $21$ boxes of "Green-heart kiwi" and "Red-heart kiwi", requiring the total expenditure not to exceed $2000$ yuan. How should the fruit store design the purchasing plan to maximize profit, and what is the maximum profit?

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