
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 chemical plant produces a certain product. When the annual output is between 150 tons and 250 tons, the relationship between the annual production cost $y$ (in ten thousand yuan) and the annual output $x$ (in tons) can be approximately expressed as $y= \frac {1}{10}x^{2}-30x+4000$.  
(1) If the total annual production cost does not exceed 20 million yuan, find the range of the annual output $x$;  
(2) Determine the output level at which the average cost per ton is the lowest, and find the lowest average cost per ton.

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