
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
In the Limin Factory, the annual production volume of a certain product is between 150T and 250T. The relationship between the total annual production cost $y$ (in ten thousand yuan) and the annual production volume $x$ (in tons) can be approximately expressed as:
$$y= \frac{x^2}{10} - 30x + 4000.$$
(I) At what production volume is the average cost per ton the lowest, and find the value of the lowest average cost per ton;
(II) If the average ex-factory price per ton is 16 ten thousand yuan, determine the production volume at which the maximum annual profit is obtained, and find the value of the maximum annual profit.

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