
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]

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[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

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In the past year of 2015, many regions in our country suffered from haze weather, which led to the hot sale of masks. The cost price of a certain brand of masks was originally 6 yuan per piece, and the selling price was 8 yuan, with a monthly sales volume of 50,000 pieces.

(1) According to market research, if the selling price increases by 0.5 yuan, the monthly sales volume would decrease by 2,000 pieces. To ensure that the monthly total profit is not lower than the original monthly total profit (monthly total profit = monthly total revenue - monthly total cost), what is the maximum selling price per mask piece?

(2) To increase the monthly total profit, the manufacturer decided to reform the marketing strategy next month. It is planned to set the selling price at x (x >= 9) yuan per piece and invest 26/5 * (x - 9) ten thousand yuan in the marketing strategy reform costs. According to market research, for every 0.5 yuan increase in the selling price per piece, the monthly sales volume would decrease by 0.2 / (x - 8)^2 ten thousand pieces. What should the selling price be per piece when x to maximize the total profit next month? And calculate the maximum total profit for the next month.

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