
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 24th Winter Olympics, the 2022 Beijing Winter Olympics, opened on February 4, 2022. The Winter Olympics mascot "Bing Dwen Dwen" made its official debut as early as September 2019 and has since become very popular, leading to the creation of many different types of mascot figurines. A certain company has undertaken the production of "Bing Dwen Dwen" toy figurines. It is known that the fixed cost of producing this toy figurine is 2 million yuan. The cost required to invest in producing x million boxes is denoted as h(x) million yuan. When the production is less than or equal to 50 million boxes, h(x) = 180x + 100; when the production exceeds 50 million boxes, h(x) = x^2 + 60x + 3500. If the selling price of each toy figurine is 200 yuan, through market analysis, the company can sell all the toy figurines. (Profit = Total sales price - Total cost price, Total sales price = Selling price × Sales volume, Total cost price = Fixed cost + Cost incurred in production)  
(1) Find the function relationship y (in million yuan) of the profit from selling "Bing Dwen Dwen" toy figurines with respect to the production volume x (in million boxes);  
(2) At what production volume in million boxes does the company maximize profit in production, and what is the maximum profit in million yuan?

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