
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
After the second World Internet Conference opened in Wuzhen, Zhejiang Province, a technology company decided to seize the opportunities brought by the internet and opted to develop and produce a large-scale electronic device. The annual fixed cost of producing this device is 5 million yuan, and the additional cost, C(x), in millions of yuan, for producing x units is given below. If the annual production is less than 80 units, then $C(x) = \frac{1}{2}x^2 + 40x$. If the annual production is at least 80 units, then $C(x) = 101x + \frac{8100}{x} - 2180$. Each device has a sale price of 100 million yuan, and market analysis confirms that all produced devices can be sold.

1. Determine the function expressing the annual profit y (in million yuan) in terms of the annual production x (units).
2. At what annual production quantity will the company maximize the profit on this electronic device?

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