
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
The 19th Asian Games will be held in Hangzhou in September 2023. The theme of this Asian Games is "green, intelligent, thrifty, and civilized", showcasing the beauty of Hangzhou's ecology and culture, fully leveraging the traction effect of international major events on urban development, thereby promoting rapid economic development. During the preparation, a company brought in an intelligent device for purchasers to negotiate purchases and decided to put a large number of them into the local market. It is known that the annual fixed R&D cost of this device is 500,000 yuan, and an additional 800,000 yuan is required for each 10,000 units produced. The company will produce x 10,000 units of this device within a year and sell them all. When 0 < x ≤ 20, the relationship between the annual sales revenue (in 10,000 yuan) per 10,000 units and the annual production volume x (in 10,000 units) is t = 180-2x; when x > 20, the relationship between the annual sales revenue (in 10,000 yuan) per 10,000 units and the annual production volume x (in 10,000 units) is t = 70 + 2000/x - 9000/(x(x+1)).  
(1) Write the analytical expression of the annual profit y (in 10,000 yuan) in terms of the annual production volume x (in 10,000 units) (profit = sales revenue - cost);  
(2) For how many 10,000 units of production volume does the company obtain the maximum annual profit? And find the maximum profit.

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