
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

...

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The Beijing-Zhangjiagang Bid Committee for the 2022 Winter Olympics held a press conference in Sochi, Russia. In order to bid for the endorsement of related activities, a company decided to evaluate one of its products. The original price of the product was 25 yuan per piece, with an annual sales volume of 80,000 pieces.  
(1) According to market research, if the price increases by 1 yuan, the sales volume will decrease by 2,000 pieces accordingly. To ensure that the total sales revenue is not lower than the original revenue, what is the maximum price per piece for this product?  
(2) In order to seize the opportunity of the Olympic bid to expand the influence of the product and increase the annual sales volume, the company decided to immediately carry out a comprehensive technical innovation and marketing strategy reform for the product, and raise the price to x yuan. The company plans to invest $$\frac {1}{6}(x^{2}-600)$$ million as the cost of technological innovation, and (50+2x) million yuan for publicity expenses. Question: What is the minimum sales volume a (in millions of pieces) that must be achieved after the reform so that the sales revenue after the reform is not lower than the sum of the original revenue and the total investment? And find the price per piece at this time.

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