
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
An American smartphone brand company has a fixed annual cost of $400,000 for producing a certain phone model. For each additional 10,000 units produced, another $160,000 is invested. Let the company produce and sell x (in 10,000 units) of this phone model in one year. The sales revenue, R(x), is given by:
$$R(x)= \begin{cases} 400-6x，0＜x≤40 \\ \frac {7400}{x}- \frac {40000}{x^{2}}，x＞40\end{cases}$$
(1) Write the annual profit function in terms of the annual production x (in 10,000 units).
(2) At what production level will the company achieve the maximum profit for this phone model? Calculate the maximum profit.

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