
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
Xiangyang City's precise poverty alleviation work has entered a crucial stage. With the assistance of a certain unit, Mr. Zhang, a poor household, has transformed a sloping land and planted high-quality blueberries, which are officially on the market this year. In the 30 days of sales, 20 kilograms were sold on the first day. In order to increase sales, a price reduction measure was taken, selling 4 kilograms more than the previous day each day. The selling price of day $x$ is $y$ yuan per kilogram, where $y$ is a function of $x$ given by $y=\left\{\begin{array}{l}{mx-76m(1≤x＜20,x\text{ is a positive integer})}\\{n(20≤x≤30,x\text{ is a positive integer})}\end{array}\right.$. The selling price on the 12th day is 32 yuan per kilogram, and on the 26th day, it is 25 yuan per kilogram. It is known that the cost of planting and selling blueberries is 18 yuan per kilogram, and the profit per day is $W$ yuan (profit = sales revenue - cost). Find:

1. $m=$______, $n=$______
2. At which day of selling blueberries is the profit the highest? What is the maximum profit?
3. How many days in the 30 days of selling blueberries have a profit of at least 870 yuan?

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