
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
A certain company produces a type of electronic chip, and the annual production of this chip does not exceed 350,000 units. The planned selling price of this electronic chip is 160,000 yuan per 10,000 units. It is known that the cost of producing this type of electronic chip is divided into fixed costs and variable costs. The fixed cost is 300,000 yuan per year, and the variable cost required to produce x 10,000 electronic chips is denoted as f(x) (unit: 10,000 yuan). When the annual production is not more than 140,000 units, f(x) = (2/3)x^2 + 4x; when the annual production exceeds 140,000 units, f(x) = 17x + 400/x - 80. Assuming that all the chips produced by the company can be sold every year.

$(1)$ Write the analytical expression of the function of annual profit g(x) (in 10,000 yuan) in terms of the annual production x (10,000 units). (Note: Annual profit = Annual sales revenue - Fixed costs - Variable costs)

$(2)$ As a decision-maker of the company, in order to maximize the annual profit of the company, how many tens of thousands of units of this chip should be produced each year?

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