
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 factory produces a type of product, when the annual output is between 150 tons and 250 tons, the relationship between the annual production total cost $y$ (in ten thousand yuan) and the annual output $x$ (in tons) can be approximately expressed as $y= \frac{x^2}{10}-30x+4000$. What should the annual output be to achieve the lowest average cost per ton? And calculate this lowest cost.

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